Lambeth residents are strongly encouraged to take a Covid-19 PCR test whether or not they show symptoms.
Improved testing will begin on Saturday at Clapham, Brixton, Stockwell, West Norwood and Vauxhall.
So far, all of the confirmed cases have been ordered to self-isolate and their contacts have been identified, the Department of Health and Social Affairs (DHSC) said.
Surge testing will also begin in Cumbria, where all 12 to 30-year-olds who live, work or study in the area are strongly encouraged to take a PCR test whether or not they have symptoms.
Those of school age will be offered tests at school.
The DHSC said people in these areas should continue to use free lateral flow tests twice a week alongside the PCR test as part of the surge testing.
Meanwhile, giant jab clinics are open in London this weekend, with the Olympic Stadium, Tottenham Hotspur FC, Chelsea FC and Charlton Athletic FC among those hosting large-scale pop-up clinics for residents, with smaller events taking place at local community venues.
It comes as officials are reportedly considering removing the 10-day self-isolation for people who have been doubly vaccinated and come into contact with someone infected with Covid-19.
Time reported that Health Secretary Matt Hancock is reportedly keen to replace quarantine with daily testing, but the policy will not be approved until after Professor Chris Whitty, England’s chief medical officer, is satisfied with the results of a study of 40,000 people.