So many crimes are being committed by eastern European migrants that police officers are being sent on courses to learn Polish and Russian.

Cambridgeshire police has paid for 50 of its staff to attend language schools because dealing with foreign suspects takes up to three times longer than dealing with British cases. The trend is further evidence of mounting pressure placed on the police by the arrival of hundreds of thousands of migrants since the European Union expanded four years ago.

Last month Jacqui Smith, the home secretary, was told by senior officers that the bill for police translators alone had soared from £14m to £24m from 2004-6.

Julie Spence, chief constable of Cambridgeshire, warned last week that the arrival of hundreds of thousands of eastern Europeans in the county, mainly for agricultural work, had left her own force underresourced and could spark “civil unrest” as the economic slowdown bites.

Arresting and processing a British suspect takes four to five hours. “With a foreign national you may have to bring in an interpreter and have documents translated – that clogs everything up,” Spence said. “As a result, it can take an officer the whole shift plus overtime to get it done. That means you don’t have your policemen out on the streets doing what they were four years ago.”

Cambridgeshire’s spending on interpreters has quadrupled since 2002 to £1m a year. Other forces using language tuition include Sussex and Gloucestershire. Nine officers from Avon and Somerset recently spent two weeks in Poland to improve their relationship with migrants.

A national police study has concluded that immigrants have not led to a crime wave, but Spence said mass migration had diverted her officers from routine neighbourhood policing to “international crimes”, such as human trafficking, drug factories and forced labour.

The number of foreign nationals detained by Cambridgeshire police has risen fourfold in the past four years. In 2006 the force arrested 942 Lithuanians and 524 Poles.

Times Recommends

• Scientists iron out mystery of our wrinkles
• My alcoholic boy, facing death at 22
• Fraud at the heart of Buckingham Palace