To take legal action. A teenager has been arrested on suspicion of murdering a 16 year old girl, leonne weeks, who was found yesterday on a pathway in rotherham. And how Donald Trumps latest tweet in praise of his daughter, ivanka, woman in brighton . Woman in brighton. And coming up in the sport on bbc news, another good day for british players at the australian open, with Heather Watson among those to progress to the second round. Good afternoon and welcome to the bbc news at one. The Prime Minister says the uk will leave the european Single Market when it quits the eurpoean union. In her long awaited speech on the impact of britain leaving the eu, theresa may said instead she would seek a bold and ambitious new Free Trade Agreement with europe for a global britain. Mrs may also confirmed that any final deal could be phased in, and that both Houses Of Parliament will get to vote on it. Well be getting political and business reaction, and explaining what it will mean for the uk. But first, our political correspondent, iain watson, on theresa mays vision of brexit britain. Good morning, what is the plan . You have had the slogan, brexit means brexit and today we saw some of the substance. Theresa may voted to remain in the European Union but she consulted leading leave campaigners. Whats the plan for brexit . Boris johnson and david davies, over the most important speech and she has made since becoming Prime Minister. She didnt give a detailed plan for brexit but she set out a direction of travel. Not partial membership of the European Union, Associate Membership, or anything that leaves us membership, or anything that leaves us half in, half out. I want to be clear, what i proposing cannot mean a membership of Single Market. Inside the european Single Market there are no trade barriers, no ta riffs there are no trade barriers, no tariffs between Member States but they have to abide by common rules, including the Free Movement of people as well as goods, making it difficult to limit immigration. The Prime Minister said she wanted a free trade deal with the eu, but control of uk borders is politically important. The message to the public before and during the Referendum Campaign was clear, brexit must mean control of the number of people who come to britain from europe. She said britain would have to come out of some aspects of the eu Customs Union, or possibly leave entirely. It imposes a charge on products coming from outside the eu. Full membership would limit the ability to do the kind of trade deals that the Prime Minister favours. To do the kind of trade deals that the Prime Minister favoursm to do the kind of trade deals that the Prime Minister favours. It is true that full Customs Union membership prevents us from negotiating our own Comprehensive Trade deals. I want britain to be able to negotiate its own trade agreements. But i also want tariff free trade with europe and cross border trade there to be as frictionless as possible. There were changes the government wants to make in the relationship with the eu, the Prime Minister hinted she wanted to give businesses time to adjust. Prime minister hinted she wanted to give businesses time to adjustm is in no ones interests for there to bea is in no ones interests for there to be a cliff edge to businesses or eight threat to stability as we change our existing relationship. The Prime Minister has given us more clarity today but she has also given more ammunition to her opponents to their attack, previously announcing state m e nts their attack, previously announcing statements such as a red, white and blue brexit. Today, the Battle Lines Of Brexit seem more firmly drawn. Through the speech there seem to be the implied threat that if all the optimism of a deal with the European Union didnt work, we would move into a low tax corporate taxation, Bargain Basement economy on the shores of europe. I think the Prime Minister mustnt wave the white flag and give up on membership of the Single Market. If she cares about britains future, if shes going to fight our corner, she must be fighting for britain to be in the Single Market even if we leave the European Union. The really difficult bit for the Prime Minister will be to persuade the other 27 member countries to listen to the uks demands. She has made it clear that no deal would be better than a bad deal and mps will get the final say. Iain watson, bbc news. So the Prime Minister has confirmed that britain will leave the Single Market, and wants a different relationship with whats known as the european Customs Union. But what exactly does that mean . Our economics correspondent, andy verity, is here to explain. The reason this is economically important is because we sell more goods and services to the 27 member countries of the European Union than to anywhere else. Its our biggest trading partner, not least because its our closest trading partner, with nearly half our exports going to eu member countries. If youre a british exporter, its very obvious what the Single Market means. Whatever you make in the uk, you can sell anywhere in the eu, no Member Country can block you. Thats Free Movement of goods. You can also invest capital anywhere, and any Member Country can invest in your country, Member States promise not to block that either. And in theory at least, you also have Free Movement of services. And, more controversially, Free Movement of people. The fear is if we leave the Single Market, our exporters wont be able to sell as much to our main trading partner, so the economy will grow more slowly. Thered be a similar effect if we left the Customs Union. Before the eu, countries used to try to stop cheap imports undercutting their own industries, especially with high value goods like cars. Theyd slap a tariff on, a form of tax to make the goods more expensive. Under the Customs Union, members of the eu agreed to scrap tariffs on each others goods. But if we exit the Customs Union, those tariffs might come back, making for example, our car exports less competitive. Thats one reason the pound dropped so sharply here after the referendum, because of fears wed export less, damaging our economy. The pounds lost about a fifth of its value and thats started to drive up prices. To this heathrow based haulier, the effect is obvious, because the pound is weak and you need more pounds to buy the same goods in dollars. Fuel had been falling in price but on todays Inflation Numbers it is up by 10 . Todays Inflation Numbers it is up by io . The company can absorb the cost but not for ever. The cost of the fuel starts to bite and eventually will have to put in a Fuel Surcharge like everybody else in the industry. When we go past a certain level. We cannot afford to keep the costs in house. The effect of the weaker pound is most obvious up of the weaker pound is most obvious up the of the weaker pound is most obvious he supply of the weaker pound is most obvious up the supply chain where raw materials, mostly imported, have gone up by 15. 8 . So far producers havent passed this on with prices up havent passed this on with prices up 2. 7 . Only now is that starting to feed through to shop prices, up i. 6 . To feed through to shop prices, up 1. 696. Sterling is happening an impactand we 1. 696. Sterling is happening an impact and we are seeing factory gate data pushing upmarket lee and Thatis Gate Data Pushing Upmarket Lee and that is the fall in sterling since the brexit vote that is driving that. The biggest impact has yet to come because contracts have to be renewed and that is when we think inflation moves up much furtherfrom the 1. 6 weve seen today, above 3 . Food prices are lower than they were last year but goods prices generally had been falling for most of the last two years and they arent any more. The return of inflation may be temporary, or if workers start demanding higher wages it could become permanent. The weak pound has prompted us companies who do a lot of business in the uk to bump up their prices. It may be making the same money or more in the uk in pounds but when that is exchanged for dollars it is much less, so the likes of apple are raising uk prices to make up. An application costing 79p will cost 99p, a 25 rise. Lets speak to our assistant political editor, norman smith. It has been a Long Time Coming but finally some fresh on the bone, the Prime Ministers vision of post brexit britain. Prime ministers vision of postbrexit britain. I think we are a bit furtherforward. Weve postbrexit britain. I think we are a bit further forward. Weve learned a bit further forward. Weve learned a bit further forward. Weve learned a bit today but we absolutely have not been given mrs mays blueprint for brexit. She was not drawing back the curtains on her master plan for leaving the European Union. We learned, yes, we are leaving the Single Market, something that many would say has been inevitable since mrs may signalled she wanted to end Freedom Of Movement and the jurisdiction of the european court. Mps are going to vote on the final deal and mrs may is not interested in some sort of Associate Membership of the union. But on key areas such as immigration, willie we are no further forward. She as immigration, willie we are no furtherforward. She said as immigration, willie we are no further forward. She said she wanted to reduce the numbers but no clarity on the mechanism for doing so. On Customs Union, she said she wanted the benefits of being outside, to negotiate trade deals but she wanted the benefits of remaining inside to ensure tariff free trade. Similarly ona ensure tariff free trade. Similarly on a possible transitional deal, she said she wanted to avoid permanent purgatory, but no clarity on the time we may have for the transitional period. The reason for this ambiguity in these key areas is because mrs may is deeply wary of revealing her intentions to our eu partners ahead of the critical negotiations. She said she will not be pressed into revealing more than she has two, if she fears is going to damage the national interest. There are, i suggest, two other reasons we didnt learn more. One, there is still active debate and discussion and disagreement within government over critical areas like immigration and finally, mrs may is instinctively a cautious politician who is reluctant to reveal more than she absolutely has to do. Norman smith, thank you. Lets speak our correspondent in brussels, gavin lee. Mrs may warned europes leaders that no dealfor britain mrs may warned europes leaders that no deal for britain was better than a bad deal. What we action so far . There are two take aways from it, the fault is a bit clearer. I spoke to different ministries where they thought that the Single Market may be something that britain would like to remain in the fog is clearer. It allows the Negotiating Teams for the eu to converge on a position before the negotiations start proper when article 50 is triggered. Early reaction around capitals within an hour of the speech. In germany the Foreign Ministry said they welcomed the clarity of seven months, they can work out a good deal. From latvia and the czech republic, they believe this is a good first opener from theresa may. The former Swedish Foreign minister saying that this wave mistake and this is not what he wa nted wave mistake and this is not what he wanted to see and that for sweden this will worsen relations between britain and the eu. I dont think this is entirely flattering. No comment from the main institutions, the european commission. We are told in strasbourg that many commissioners were watching the speech a short while ago so i think through the afternoon we will see how the European Union acts the reacts but we will find out more. So whats the reaction from business leaders, many of whom are in switzerland for the annual World Economic forum . Our business editor, simonjack, is there. What has been the reaction so far . We got a very clear message, no ifs, no buts, no Single Market and as norman was saying, most companies had conceded, it is and what they wa nted had conceded, it is and what they wanted but they have accepted that reality as being incompatible with ambitions to control migration. Interested to hear more detail on the transitional period, what happens two years from triggering article 50. She said we wont have some never ending standstill agreement, where we keep negotiating, we want the deal struck within two years with some Implementation Phases so everyone can get used to the idea. Businesses are worried that getting the deal in principle in two years is unrealistic and what we might do is fall off a cliff into this regulatory and trade no mans land and people have warned that would be damaging. Interesting that she repeated the threat that Philip Hammond raised, that if we dont get a good deal, if you play hardball, we can lower taxes and change the economic model, becoming a lower Tax Jurisdiction for multinational companies. Some people would say that this isnt what people voted for, but that is the aggressive tone. Businesses are worried that the timetable she has for completing the timetable she has for completing the deals is a bit unrealistic. Thank you forjoining us. What about the voters . Six months after the referendum, what do people make of mrs mays speech . Our correspondent, phil mackie, has been to birmingham, where people voted by a narrow margin to leave the European Union. When the country voted to leave the eu last year, it was a close vote nationally, 52 in favour of brexit, 48 in favour of remain. In birmingham, it was even closer. Half a Million People went to the polls in this city and the winning margin for leave was onlyjust under 4,000 votes. So now people have an inkling of what brexit means, what do they think . Andy and debbie are typical. One voted leave, the other remain. If its too high a price to remain in the Single Market in terms of the price we have to pay for immigration, its a Fair Trade Off in my opinion. Im afraid to say that although i voted to stay in, it probably makes sense because going forward, if were out, were out. Making the coffees are maria from slovakia and veronica from hungary. Both might be allowed to stay, but in the future for people wanting to work here, life could be more difficult. I would like to choose what country i want to live in or work in. So if i have to leave just because of brexit, i wouldnt like it. The salary is much better than hungary, even for the same job. And for the english manager of this independent coffee shop, tougher Border Controls would mean a real headache when recruiting staff. One out of ten cvs that come over the counter on a weekly basis are european, so if that was restricted, it would be difficult to recruit people, especially full time members of staff that are hard to come by. For many in the second city, the prospect of brexit is still filled with optimism, but in a city thats so evenly split, others are still left with a bitter taste. Phil mackie, bbc news, birmingham. A libyan man has won the right to sue the british government, including the Foreign Secretary at the time, jack straw, over claims of kidnap and torture. Abdul hakim belhaj, a former opponent of colonel gaddafi, was arrested in bangkok, taken to libya and questioned by agents from mi6 and the cia. Mr straw has denied any involvement. Heres our home affairs correspondent, tom symonds. Coming up in sport at half past, six time Paralympic Champion david weir says hell never race for Great Britain again after voicing his frustration with governing body british athletics. The inquests into the death of 30 british tourists at a Tunisia Beach Resort 80 months ago is under way this morning. The court has been hearing from a Senior Foreign Office official who has been defending the Travel Advice to the country at the time. Our correspondent Richard Galpin has the latest. Day two of the inquest, and for the families of those killed, a chance to hear more crucial testimony from the Foreign Office and from the Tourism Company which sold them the holidays in tunisia. These are the 30 british Holiday Makers who were killed in the attack. Could more have been done to warn them of the risks of travelling to Tunisia Injune 2015, just months after a major Terrorist Attack in the capital . This video played in the courtroom yesterday shows the gunman, seifeddine rezgui, arriving in the resort near sousse at the start of his attack, proof that he had accomplices who were probably linked to the earlier atrocity in the capital. And the way rescue was able to systematically shoot dead so many tourists has shown how little security there was at the resort, even though the tunisians had said security had been improved. Today a Senior Foreign Office official admitted they had not been formally monitoring the Security Arrangements in tunisia, but said their chocolate by stress the high risk of Terrorist Attacks, including in areas visited by foreigners. Next in lime to give evidence here will be tui, the Parent Company of thomson which sold all the Package Holidays to those who were killed. It is also likely to face some tough questions. Richard galpin, bbc news at the high court in london. An 18 year old man has been arrested on suspicion of the murder of a teenage girl whose body was found on a pathway in rotherham. The girl has been named locally as 16 year old leonne weeks. South Yorkshire Police say her body was found by members of the public yesterday morning. Our correspondent danny savage is in rotherham. What is the latest . Apologies, we dont seem to have the sounds to danny savage at the moment. The rest of the news. The search for a malaysian airliner that vanished three years ago with 239 people on board has been called off. An underwater search for debris from flight mh370 has failed to discover a significant amount of wreckage. The families of those on board say the decision to stop searching is irresponsible. The plane disappeared on its way from kuala lumpur to beijing after turning off course. One of the unions behind the southern rail strikes has agreed to suspend three days of industrial action next week while fresh talks hosted by the tuc take place. Representatives from the Drivers Union aslef will meet for talks on wednesday. The last man to walk on the moon, the astronaut gene cernan, has died at the age of 82. Iamon i am on the surface. Captain cernan was one of only three people to go to the moon twice and as commander of nasas apollo 17 mission. He was the last man to leave a footprint on the lunar surface in 1972. His death means only six of the 12 men who have walked on the moon are still alive. In four days time donald trump takes over the white house, becoming the 45th president of the united states. It marks the end of Barack Obamas eight years in the oval office. All this week, our correspondent jon kay is travelling along highway as, gauging the countrys mood. Today hes in chicago, illinois where barack obama began his political career, and where people have been reflecting on the legacy he leaves behind. Right through the middle of Donald Trumps america. To get a sense of the country he is taking over. But our next stop is not trump territory. Chicago. This is Barack Obamas favourite diner. He lived round the corner before he was president and he still comes back. He is humble, he is strong. Taihitia is an obama fan. As a nurse, she likes the changes he made to health care, giving poorer People Better access. She worries donald trump will overturn the reforms, hitting the most vulnerable. Many of them will be very sick, cant get medicine. Some of them will die. Her son daniel thought having a black president would mean a more inclusive america. But he fears Donald Trumps brand of populism is now encouraging division. I do feel my safety might be, you know, in danger. Really . You feel more vulnerable now . I do, i do. In certain situations i do. Post trump . Post trump, yes. Because it is something that you can see from the energy that trump built and the way that people express themselves who support trump. A lot of them have certain beliefs in things like that that do not align with my existence. Some here do question the obama legacy and think change is overdue. Aspiring businesswoman erika hopes donald trump will help people like her. I believe that hes going to open up doors for Small Business owners, hopefully, thats trying to create big businesses. Like you . Yes. Maybe you will be as rich as donald trump in a few years . We head to the suburbs. Elgin, where nearly half the population is hispanic. Donald trumps plans to build a giant wall along the Mexican Border mean many here cannot support him. Never. But some views here may surprise you. Rosa hopes a wall would help stop illegal immigrants. We have our own problems here in america, so. You know, to add more of them coming over here, i think. I dont think its a good thing. And in the choir, margarita hopes donald trump will safeguard her pro life catholic values. Im so excited and im so happy for him. And we should not be afraid of anything, not even a wall or anything. It seems this Hispanic Community is split, just as america is split. And look where we are. Time to get back on route as. Jon kay, bbc news, chicago. And Tomorrowjon Kay continues his journey down route as. Hell be in tennessee. Its a month since Syrian Government forces re took rebel areas of the countrys second city, aleppo. Now new peace talks are due to Begin Next Week between the Syrian Government and some of the rebel groups whove been fighting against president assads regime for the last six years. Well we can talk now to our middle east editor, jeremy bowen, who is in aleppo. Describe what life is like theyre now, jeremy . In the eastern sections of the city that were captured by the regime, life is really very hard. No running water, no mains power and a massive amount of devastation. What you see behind me isa devastation. What you see behind me is a tiny fraction of what has happened in this city. You can drive a couple of miles in One Direction of east aleppo and everything is destroyed, a couple of miles in the other direction and everything is destroyed. It is really that bad. I have been to lots of war is over the yea rs have been to lots of war is over the years and the only place i have seen that rivals this in terms of sheer destruction is grozny in chechnya in the former soviet union in the mid 90s when the russian army absolutely hammered it. East aleppo was absolutely pulverised. Jeremy bowen with the latest from aleppo. Time for a look at the weather. Heres phil avery. An awful lot of cloud. If you were with those yesterday we were looking at this sort of satellite picture. There are variations on the scene. I wa nt to there are variations on the scene. I want to fly you towards the thick clouds and old weather fronts, if you have spent the morning underneath it like in bridlington, stafford and a number of other places, pretty miserable. Pieces of rain and drizzle. Turning towards east anglia and the south east, recent clouds, that becomes what cloud . The weather watchers are talking the talk for as admirably. If you are beginning to get a bit envious of that south eastern quarter with all the sunshine if you have not seen any so far today and are not likely to see any, it comes ata are not likely to see any, it comes at a price. Three degrees, some even lower than that, with the mild breezes over the eastern side of scotland, 13 degrees. As soon as the sun is done, the temperatures will fall away again in the south eastern quarter. With the breeze and more cloud across northern and western parts it keeps the temperatures up. The towns and cities will be around about zero, i degrees or so. In the countryside across the south east and night, a macro or five. There is something going on here. There is something going on here. The last significant influence for the south eastern quarter was tapping into a relatively cold continent. Those are the Daytime Maximum is yet again across the heart of the continent. The reason for the connection between the tumour grows a high without getting too. . . Nospace s army, there is that flow, so as was the case again, it will be dry, bright and frosty again. Breezy, wetting cloudy across the north west of scotland. The old fronts might have never voted for rain across the