Photo: Eddie Mitchell
The council said the changes were introduced "in response to concerns from residents and visitors about parking problems in the park during the day".
It comes after a petition was launched to rescind parking charges for regular walkers at the park and for an affordable annual parking permit to be offered instead.
More than 1,400 people have now signed the petition on change.org, started by pensioner Joy Flowers.
The 67-year-old said: "It seems to lots of us that the council is just not listening.
"It's a tax on exercise. There's a lot of people I know who won't be able to afford the car parking.