Foreign nationals being arrested for some crimes including robbery, burglary and theft have more than doubled in the period, figures show. In general, crimes committed by those born abroad has increased by 53 per cent.
An investigation has discovered increasing numbers of foreign nationals being detained by West Midlands Police, the country's second biggest force, which is already struggling to cope with unprecedented cuts of £125 million.
Khalid Mahmood, MP for Perry Barr, said: "There are a lot more undesirables coming in now. They see rich pickings in Britain because there are no controls."
He added: "We are a lot easier targets than the rest of Europe because of the cutbacks. We have fewer border controls and fewer internal controls."
The figures obtained by a local newspaper under the Freedom of Information Act show that 7,716 foreign suspects were arrested by the force between April 2010 and March 2011. But that figure rose to 11,801 between April 2011 and March this year.
Of those arrested, 2,629 were for violence against the person, a rise of more than 600 from the previous 12 months.
Foreign nationals were also detained for almost 400 sexual offences, up from 271, while robbery and burglary arrests more than doubled; up to 486 from 239 and up to 533 from 254 respectively.
Romanians were the most prolific offenders last year, with a of 1,329 detained. Indians were the second most likely to be arrested, with 1,156 arrests.
The numbers of Iraqi and Afghan nationals being questioned by police rose from 516 to 787. Overall, crime in the force area has fallen, with robberies dropping by 20 per cent and burglaries by 17 per cent, but there was a surge in cases involving people from Eastern Europe.
More than 1,000 Poles were arrested last year, compared with 614 the year before. Police also picked up 440 Lithuanians, up from 235, while 322 Latvians were arrested, compared with 193 from the previous 12 months.
A string of attacks carried out by Eastern European criminals in recent months has raised concerns over the lack of checks on new arrivals.
In February, a Polish burglar was jailed for at least 23 years for the murder of an elderly couple in Wolverhampton, a week after he had arrived in Britain.
Ireneusz Bartnowski, 22, stabbed and battered to death Guiseppe and Caterina Massaro after lying in wait in their bedroom and attacking them.
In January, a Lithuanian was arrested for the murder of Avtar and Carole Kolar in Birmingham.
Rimvydas Liorancas, 37, was charged with murder but was found hanged in his prison cell a month later.
It was later disclosed he was a violent criminal and illegal immigrant who had previously been kicked out of Britain.
Of the 11,800 foreign nationals arrested by West Midlands Police, 2,188 were dealt with in court last year. A total of 1,214 received cautions, while 4,433 foreign nationals faced no further action.
Ian Edwards, chairman of West Midlands Police Federation, which represents rank-and-file officers said: "Crimes should be detected and arrests made, whoever they may be.
"However, increasing arrests of foreign nationals does lead to an increasing drain on the dwindling finances of the force.
"These figures have to represent a worry to the force because many foreign nationals will require interpreters and other associated costs to a force already having to make £125 million savings by 2015, with further planned savings anticipated in the future."
A West Midlands Police spokesman said: "We police across a diverse range of communities in the West Midlands.
"Overall, we have seen significant decreases in both burglary and robbery - people are safer now than they have been at any time during the last 10 years.
"Robbery is down by a third so far in 2012 with 1,204 fewer robbery victims between April 1 and September 10 compared to the same period in 2011.
"Similarly, there have been 1,241 fewer burglaries during the same period this year.
"Residents can feel safer in their own homes."