Some cases of the Covid variant first identified in India have also been found in the borough.
The council is urging people living, working or studying in the Brixton and Stockwell areas to have a Covid-19 PCR test.
Testing sites are open from May 27 for 10 days in Windrush Square, Brixton and from May 28 at Stockwell Memorial Gardens. Both sites will be open from 9am to 3pm.
The move follows case data showing the incidence rate in Lambeth has increased in recent weeks from around 10 cases per day, to between 20 and 30 new infections being detected per day.
Similar measures were put in place in Clapham on May 22. Testing there, in Windmill Drive, will continue until June 1.