Following surveillance activity, a small number of cases of the variant first identified in India, have been found in the Kingsbrook area of Aylesbury.
The people involved have self-isolated and followed all of the recommended guidance.
A spokesman for Buckinghamshire Council said: "We are asking all Kingsbrook residents, businesses and visitors in the HP22 7AA to HP22 7BP postcode areas to undertake PCR testing so that we can help avoid the spread of this variant and understand whether it is spreading in our community.
"Testing will, in combination with measures such as hands-face-space-fresh air and current lockdown guidelines, help to suppress and control the spread of the virus, while enabling a better understanding of the new variant."
These PCR tests should be done even if people are not showing any symptoms, they have previously had Covid-19, or they have had a Covid-19 vaccination, says the council.
Aylesbury has strong links with Milton Keynes with many local students going to grammar schools there and adults commuting to MK to work.