Police said officers had been called to break up a garden party over the weekend.
Royal Wootton Bassett Police took to Facebook to urge people to stay at home.
They said officers received a number of complaints of people “conducting extended non-essential shopping trips” on Sunday afternoon and “also had to break up a garden party”.
Two men, aged 28 and 33, were each fined £60 after they were found in the same car on Royal Wootton Bassett’s High Street.
Officers wrote: “Please help us look after everyone and spread the message of staying at home.”
On Sunday, Chief Constable Kier Pritchard urged people to stay at home: "I know that many people will be feeling fatigued and some may become complacent and consider the risks worth taking. We all must take responsibility for our actions - please stay home, stay safe, protect the NHS and save lives."
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