The Government has tried to reassure people that immigrants cannot jump housing queues by launching new guidance for councils.
Local authorities are to be ordered to dispel "myths" about housing allocation in their communities.
But they will not be given powers to prioritise long-term local residents - as Gordon Brown suggested last month.
The initiative is part of a "fairness" drive as the Prime Minister seeks to rejuvenate his Government.
The draft guidance makes clear that the most important factor in handing out housing will still be need. But councils will now be able to take other elements into account, such as how long people have been on waiting lists and skill shortages in the local area.
There will also be a crackdown on fraudsters who get housed at the taxpayer's expense, and then sub-let to earn extra cash.
Housing minister John Healey said: "People must have more confidence that decisions about who gets housing are taken fairly. This means better information for residents, so that local authorities' allocation policies are clear, well understood and meet the needs of the whole community. It also means councils making the most of the greater leeway I'm giving them in the new guidance to allocate homes according to local needs.
But shadow housing minister Grant Shapps hit back: "Rather than constantly reshuffling housing Ministers to dream up new headlines, they should focus on bringing real help to the five million people now on the record housing waiting list. For more than a decade they have simply failed to build enough homes in this country and now the chickens are coming home to roost.
Far-right parties have exploited the perception that immigrants get priority access to housing.
However, a report by the Equality and Human Rights Commission earlier this month found there was "no evidence" foreigners were able to jump queues.