Coronavirus cases in Bedford have tripled in the last few weeks as the Indian variant has been identified in the town.
The Borough Council said seven cases have been found among young people and is working with Public Health England (PHE) to investigate them.
So far, it is not know how the strain arrived in the town, but extra testing of close contacts will be carried out at two schools as well as targeted testing.
"We do need to do some more investigation to find out the extent to which the Indian variant is at the root of this and that is why we are doing some very targeted testing at the moment", Cllr Jackson added.
"So those families who have been identified as needing to be tested will have been contacted and should attend the test centre that they have been asked to.
"This is obviously a variant of concern and that is why we are taking the action we are taking."
Surge testing or mass testing of communities is not currently required.
Health bosses are urging people to get vaccinated and continue to follow Covid rules.
"Hopefully we can get this under control but we are not at the end of this yet and I think it is really important that everybody recognises that and continues to do everything they have been doing to suppress this virus", Cllr Jackson said.
"We have a better handle on things as we did right at the very start of the pandemic, so that is encouraging but we have to continue to observe the rules, stay outside, even though it is miserable."
People without symptoms can drop in to the rapid test centre at the Faraday Community Centre, from 7am on Tuesday 11 May. No appointment is needed and results come back in less than an hour. Home test kits can also be collected from the test centres, some pharmacies and libraries.
Anyone with symptoms should self-isolate and book an appointment for a PCR test.
More details on testing is available on the council’s website www.bedford.gov.uk/covid-19-testing/