Telford & Wrekin Council said that "several" of the 39 new cases of coronavirus in the borough (recorded between April 26 and May 2) are linked to cases in Hadley and Leegomery.
A statement from the council said: "Once again, coronavirus cases in Telford and Wrekin remain low, but we are continuing to monitor closely the mutation of the UK variant in Hadley and Leegomery.
"The huge community effort in Hadley and Leegomery to get tested goes on. Thank you to those who have been tested. Each test helps us to track and stop the spread of the virus.
"Several of the new cases this week can be linked to the cluster of cases in Hadley and Leegomery. We don’t know yet if these new cases have the mutation of the UK Covid-19 variant, but each of these cases will be sequenced in a laboratory to confirm who has the mutation.
"The following people are being asked to take a PCR Covid-19 test, even if they are not showing symptoms: families with school aged children in Hadley and Leegomery; their extended families, friends, bubbles; and residents in Hadley and Leegomery."
Book a Covid test at gov.uk/get-coronavirus-test.