Newham Council says it can no longer afford to house tenants on its waiting list in private accommodation.
The gap between market rents and the housing allowance is too big, it says.
But the association says such a move could mark the start of “thousands of needy people” being dumped elsewhere.
Labour MPs say the decision to seek accommodation outside London is proof that the government’s policy of capping housing benefit is already “beginning to unravel”.
Newham Council, which is Labour-controlled, is in the east of the city and will host this summer’s Olympics.
It has written to the Brighter Futures Housing Association in Stoke, offering it the “opportunity” to lease homes to it.
The letter says the local private rental sector is beginning to “overheat” because of the “onset of the Olympic Games and the buoyant young professionals market”.
It says the council can no longer afford to house tenants on its waiting list in private accommodation as the gap between market rents and the local housing allowance has become too great.
The council has been “forced to look further afield for alternative supply”, it adds.
The Brighter Futures chief executive officer, Gill Brown, has not formally replied to Newham Council’s offer but says she will not agree.
Newham – along with other London councils – is under significant pressure”
Newham Council Spokesman:
“I think there is a real issue of social cleansing going on,” she said.
“We are very anxious about this letter which we believe signals the start of a movement which could see thousands of needy people dumped in Stoke with no proper plan for their support or their welfare.
“We have seen in the past relocation putting strain on other services because the medical, education and justice systems are unprepared for an influx of very needy people.
“The result was huge, unplanned pressure on local services, the collapse of already vulnerable neighbourhoods and the rise of divisive right-wing extremism.
“We believe that, if London boroughs are allowed to export their most vulnerable and challenging families to cities like Stoke-on-Trent, then exactly the same will happen again.”
A spokesman for Newham Council said the government’s decision to cap housing benefit payments at £400 per week for a four-bedroom home was “exacerbating the problem” of finding homes for low-income families.
“Newham – along with other London councils – is under significant pressure,” the spokesman said.
“We are doing everything we can to ensure we have good quality, affordable housing which is fairly distributed.
“Alongside a number of other London councils, we are also exploring the option of working with housing associations outside the borough to house people with an immediate need in the private sector, when there is no other alternative.”
Newham Council is offering to pay Brighter Futures 90% of the local housing allowance plus £60 per week.
Brighter Futures estimates the scheme could save Newham Council £5,250 a year for a family housed in a three-bedroom home.
The Labour MP for Westminster North, Karen Buck, says Newham Council’s offer could be just the tip of the iceberg.
“An unplanned influx of Olympic exiles will do us little good”
Tristram Hunt, Labour MP for Stoke-on-Trent Central:
“What is so worrying about the letter from Newham is not that this is Newham Council’s fault but if a very poor borough in east London feels itself so desperate that it has to try and find accommodation as far away as Stoke, what is that telling us about demand?” she said.
“We know from London Councils that 88,000 households have private rents above the new limits for housing benefit and in theory these families were meant to find new homes in places like Newham.
“Obviously, even before the housing benefit cuts have really began to bite we have seen that this policy will unravel.”
When the housing benefit cap was announced in 2010, London Mayor Boris Johnson said: “The last thing we want to have in our city is a situation such as Paris where the less well-off are pushed out to the suburbs.”
He said he would “not accept any kind of Kosovo-style social cleansing of London”.
The Labour MP for Stoke-on-Trent Central, Tristram Hunt, says the rest of the country “certainly doesn’t need the difficult-to-house cases London boroughs have had enough of”.
“An unplanned influx of Olympic exiles will do us little good,” he said.
“The 2012 Games are bringing huge riches into London. The least those boroughs could do is look after their poor and needy.
“We look forward to welcoming the flame from Stratford – but not east London’s exiles.”
Brighter Futures is calling on the Local Government Association to draw up a code of conduct for members to ensure that no homeless people are moved without the permission of the council in the new area.
It wants to ensure local councils have assessed whether public services can cope with new arrivals before families are moved.