People aged 11 and over are being urged to take a PCR test even if they have no symptomsWandsworth and Lambeth will see additional testing after 44 confirmed and 30 probable cases were identified.
The Department of Health and Social Care (DHSC) called it the "largest surge testing operation to date".
All identified cases are isolating or have completed their isolation and their contacts have been traced.
Dr Susan Hopkins, chief medical adviser for NHS Test and Trace, said the number of cases was "significant" and stressed it was "really important people in the local area play their part in stopping any further spread within the local community".
The Mayor of London, Sadiq Khan, urged people in the affected boroughs to get tested "as soon as possible".
"It's vital that we do everything we can to control this variant by taking a test and following the rules," he said.
People aged 11 and over who live, work or travel through the affected areas are being urged to take a Covid-19 polymerase chain reaction (PCR) test, as well as using twice-weekly rapid testing.
Positive results from PCR testing will be sent for genomic sequencing at specialist labs.
The PCR test has been advised as well as using twice-weekly rapid testing
The first case was found in early March and the DHSC said the testing operation was aimed at suppressing any possible new cases of the variant.
Dr Hopkins said: "Around one in three people with Covid-19 don't show any symptoms.
"By taking part you can protect yourselves and your loved ones and help us identify any possible new cases that would otherwise be missed, preventing further transmission and saving lives.
"Surge testing was previously carried out in three postcodes of Lambeth after a case of the South African variant was discovered.
In March, intensive testing was put in place in three areas of Wandsworth borough following a small number of cases.
