Surge testing has started in Bedford due to an increase in coronavirus cases linked to the Indian variant.
Health Secretary Matt Hancock said the town was the "next biggest cause of concern" after Bolton and Blackburn with Darwen.
Bedford has the second-highest rate of Covid-19 in England, with cases doubling every five days.
"I would urge everybody in Bedford to exercise caution and engage in testing," Mr Hancock said.
Surge testing has started at two schools in Bedford.
Mr Hancock told the House of Commons early evidence suggested the Indian variant was more transmissible than the Kent variant.
At present there is no evidence that the Indian variant is resistant to current vaccines.
Mr Hancock said there were 2,323 confirmed cases of the variant in the UK - of which 483 were in Bolton and Blackburn with Darwen.
Last week, Bedford Borough Council called for vaccines to be offered to all residents aged 16 and over due to the increase in cases.
Professor Chris Whitty, England's chief medical officer, said local "surge vaccinations" were not being pursued as there was a "finite" supply of doses and younger people were less at risk from the virus.
Louise Jackson, portfolio holder for public health and wellbeing at the council, said she thought not offering vaccines to people aged over 16 was "a mistake".
"We have the second highest rate of infection in the country," she said.
"We should be getting the resources and vaccinations here so we can get on top of things."
While discussing the variant in the House of Commons, Mr Hancock urged those eligible to get the vaccine.
He said the majority of people who had been admitted to hospital in Bolton had been eligible for the jab but had not taken it up.
"It just reinforces the message that people should come forward and get vaccinated because that is the best way to protect everybody," Mr Hancock said.