Surge testing has begun after "a very small number" of cases of the South African variant were found in part of Norfolk.
People in Diss and the nearby village of Roydon have been urged to get a Covid-19 test, regardless of whether they have symptoms.
It was hoped 10,000 would be tested in the next two weeks, Norfolk County Council's public health team said.
Testing can being carried out at mobile units or with a kit at home.
The council said a "very small number" of people in the Diss and Roydon area had tested positive with the South African variant, and they were all self-isolating.
A council spokesman said it was "government policy to bring in surge testing for any cases that can't be linked explicitly to foreign travel, regardless of how small the number is".
Mike Pursehouse, from South Norfolk Council's corporate management leadership team, said it was an exercise in logistics.
"We have a strong team - South Norfolk Council put the boots on the ground... Norfolk County Council with public health doing the infrastructure, a huge array of NHS staff," he said.
"The police are working with us to keep us safe as well, so [in total] we've got 25 staff a day in Diss and Roydon."
The programme involves PCR Covid-19 tests, which, unlike lateral-flow testing, means swabs are sent to a lab in Thetford for analysis.
The authorities hoped the results would give a detailed picture of how the South African variant arrived in the area, and how it was spreading.
Tests can be booked with mobile units deployed at:
- Diss Youth and Community Centre, (19-25 February, opening 09:00-15:00 GMT)
- Roydon Community Centre (19 February to 4 March, opening 12:00-18:00)
- Diss Leisure Centre (19 February to 4 March, opening 09:00-15:00)
Vulnerable people can request to have a test delivered and collected from their home.