Ministers and union chiefs warned against the demonisation of migrant workers after a senior police officer asked the Government for more money to deal with new arrivals.
Julie Spence, Chief Constable of Cambridgeshire, said the vast majority of newcomers were law-abiding, but cited a 17-fold increase in the number of foreigners arrested for drink-driving in one year.
She also said there was an "international dimension" to such crimes as cannabis production, human trafficking and credit card skimming.
But Liam Byrne, the Immigration minister, said Cambridgeshire police had received a 20 per cent funding increase over the past decade and had seen a 20 per cent drop in crime. He added: "I think we've just got to be quite careful about singling out any particular section of society."
Downing Street also distanced itself from her comments. Gordon Brown's official spokesman said: "If you look at what's happening to total crime in Cambridgeshire, it's been on a clear downward trend."
Brendan Barber, TUC general secretary, said: "There are criminals in every community, but we need to recognise that migrants are often exploited."