It comes after two new cases of the South African variant were discovered in Redbridge.
Testing will now begin across the IG1 and IG6 postcodes, and will take place in small areas of the IG5 and IG7 postcodes.
Everyone over the age of 11 in these areas is being urged to take a test to help prevent the spread of the new variant.
The two outbreaks are not believed to be linked, the Department of Health said.
There are currently four variants of concern in the UK.
These are the the South African variant, two different Kent variants, and the Brazilian variant (carries E484K).