Bedford Borough Council has been notified of seven cases of the variant known as VOC-21APR-02 - known commonly as the 'Indian' variant because it was first identified in India.
The variant was identified after genetic sequencing was carried out on positive Covid-19 tests.
The council is working closely with Public Health England to investigate the cases and as a precautionary measure, additional testing of close contacts will be carried out at two education settings in the Borough.
Surge testing or mass testing of communities is not currently required.
Vicky Head, Director of Public Heath for Bedford Borough said: “Public Health England notified us that it had identified cases of the variant known as VOC-21APR-02 in Bedford Borough.
"PHE has already been in touch with the people concerned to ensure they are self-isolating and to complete contact tracing.
“Since then we have been working closely with the education settings and PHE to ensure that all close contacts of those affected are identified and advised to self-isolate for 10 days.
"Targeted testing is also taking place as a precautionary measure.
“There is currently insufficient evidence to indicate that this variant causes more severe illness or renders the vaccines less effective.
"We will continue to work with our education settings to ensure they remain as safe as possible for our children and young people.
“It is important to remember that the virus has not gone away and I would urge everyone to continue to be cautious.
"The best way to help stop the spread of the virus is to continue to follow the guidance – Hands, Face, Space and Fresh Air.
“If you do meet others this weekend, please make sure you follow the rules, and stay outdoors whatever the weather.
"Everyone in the Borough is encouraged to take up the offer of twice weekly testing so that we can stop the spread of the virus.”
People without symptoms can drop in to the rapid test centre at the Faraday Community Centre, from 7am on Tuesday, May 11. 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.