The following correction was printed in the Observer's For the record column, Sunday October 31 2010

This article said: "From October 2011 payments will be capped at 30% of average local rents." In fact, payments will be capped at the 30th percentile of local rents. This means they will be no higher than the lowest 30% of local rents.

Ministers were accused last night of deliberately driving poor people out of wealthy inner cities as London councils revealed they were preparing a mass exodus of low-income families from the capital because of coalition benefit cuts.

Representatives of London boroughs told a meeting of MPs last week that councils have already block-booked bed and breakfasts and other private accommodation outside the capital – from Hastings, on the south coast, to Reading to the west and Luton to the north – to house those who will be priced out of the London market.

Councils in the capital are warning that 82,000 families – more than 200,000 people – face losing their homes because private landlords, enjoying a healthy rental market buoyed by young professionals who cannot afford to buy, will not cut their rents to the level of caps imposed by ministers.

The controversy follows comment last week by Iain Duncan Smith, the work and pensions secretary, who said the unemployed should "get on the bus" and look for work. Another unnamed minister said the benefit changes would usher in a phenomenon similar to the Highland Clearances in the late 18th and early 19th centuries, when landlords evicted thousands of tenants from their homes in the north of Scotland.

In a sign that housing benefit cuts are fast becoming the most sensitive political issue for the coalition, Jon Cruddas, the Labour MP for Dagenham, last night accused the government of deliberate social engineering.

"It is an exercise in social and economic cleansing," he said, claiming that families would be thrown into turmoil, with children having to move school and those in work having to travel long distances to their jobs. "It is tantamount to cleansing the poor out of rich areas – a brutal and shocking piece of social engineering," Cruddas added.

The National Housing Federation's chief executive, David Orr, described the housing benefit cuts as "truly shocking". He said: "Unless ministers urgently reconsider these punitive cuts, we could see more people sleeping rough than at any stage during the last 30 years."

The issue is fuelling tension inside the coalition. Simon Hughes, the Liberal Democrat deputy leader, said last night he would table amendments to change housing benefit rules. He said: "I would fully expect to be one of those putting forward proposals for changes in the housing benefit rules, particularly for London."

Under a clampdown on housing benefit, the chancellor, George Osborne, announced that housing benefit will be capped from April next year at £400 a week for a four-bedroom house, £340 for a three-bedroom property, £290 for two bedrooms and £250 for a one-bedroom property. In addition, from October 2011 payments will be capped at 30% of average local rents.

At a meeting of the Commons work and pensions select committee last Wednesday, the day Osborne announced £81bn of cuts in the spending review, MPs were told by London council chiefs that the housing benefit cuts could have devastating results.

Nigel Minto, head of sustainable communities at London Councils, who works closely with the capital's housing directors, told the committee that since June London councils had been "procuring bed and breakfast accommodation" in outer London and beyond. The committee was told similar problems would occur in other cities with high-priced property such as Brighton and Oxford.

Jeremy Swain, chief executive of the homelessness charity Thames Reach, said he was particularly worried about the impact on numbers sleeping rough in London. "We have reduced rough sleeping dramatically and we have a target of zero rough sleeping in London by 2012. For the first time I'm thinking that we will not achieve that," he said.

Karen Buck, shadow minister for work and pensions, said: "The sheer scale and extremity of the coalition proposals means almost a million households are affected across the country."

In today's Observer, Labour leader Ed Miliband says last week's spending review took Britain back to the 80s. "This was the week that took the compassion out of David Cameron's claim to compassionate Conservatism," he writes, accusing the Tories of displaying "arrogant ideological swagger".

But last night Cameron insisted the cuts were tough but fair. "Departments have to make savings. I don't underestimate how difficult this will be. But we are doing what we are doing because it is the right thing to do – right by our economy, right for our country."

A DWP spokesperson said: "The current way that it [housing benefit] is administered is unfair. It's not right that some families on benefits have been able to live in homes that most working families could not afford. However, we are absolutely committed to supporting the most vulnerable families and have tripled our discretionary housing payments to provide a safety net for those who need it."