Once they settle and are entitled to help, it adds, the same proportion[of migrants] live in social housing as UK-born residents.
The prime minister has said guidance would change so that local people get priority for social housing in England.
Housing minister John Healey said the changes were designed to tackle the "myth" that the system was unfair.
He insisted the changes would not alter the current requirement for council housing to be awarded on the basis of need or the policy that economic migrants cannot apply for housing for the first five years after settling in the UK.
But councils would get more "leeway" to deal with specific housing pressures in their areas.
The British National Party has campaigned heavily on the issue, claiming that British people are being short-changed for housing in favour of newly arrived immigrants.
Mr Healey said it was "wrong" to say the government had been forced into action to counter the BNP`s arguments after it succeeded in getting two Euro MPs elected.
But he added that he wanted to "nail the myth" that certain groups were losing out in terms of housing allocation.
"It is largely a problem of perception," he told Today.
"The report shows there is a belief, a wrong belief, that there is a bias in the system."
Although the rules would not change, Mr Healey said new guidance to councils will enable them to help people who have been waiting the longest or those, in rural areas, who have strong local or family connections.
"There is more we can do to give local authorities more freedom and scope to give more preference," he said.
He added that changes to the system of allocation were "no substitute" for building more council houses.
Ministers say they will build an extra 20,000 affordable homes over the next two years, in addition to 90,000 already announced, but critics say this is inadequate given the four million people now on a waiting list for homes.