Officials figures suggested there had been 76 new cases in the most recent week for which data existed, between 11 and 17 July.
That was a rise of 33 on the week prior.
In a tweet, Luton Council said: “Please protect yourself and your family by booking a test even if you don’t have symptoms.”
The town’s Downside Primary School will serve as a testing site on Thursday and Friday, the authority said. Residents can walk or drive there.
Luton Council is urging residents to get tested for coronavirus after a spike in cases.
The local authority said it would put on extra testing at a primary school this week in order to track the infections.
The Independent has contacted Luton Council for more information.
Since the weekend, English councils have had the power to impose their own local lockdowns to prevent the spread of Covid-19.
“They will be able to close specific premises, shut public outdoor spaces and cancel events,” Boris Johnson, the prime minister, said as he announced the plan.
And, this week the health secretary, Matt Hancock, reversed course by allowing local public health directors access to “enhanced” granular infection data beyond the postcode level.