About 6% of social housing tenants in Britain affected by changes to benefits partly designed to cut under-occupancy have moved home, BBC research suggests.
Ministers claim the policy - dubbed a bedroom tax by critics - frees up big homes and saves the taxpayer £1m a day.
Employment Minister Esther McVey said the government was "on track" to reach its target of 30% by 2017.
Shadow employment minister Stephen Timms said the policy had been a "disaster" and should be scrapped.
BBC analysis of the data from social housing providers also suggested 28% of affected tenants were in rent arrears for the first time in the past 12 months.
But Ms McVey disputed this figure, saying feedback from local authorities and the National Housing Federation had found an "indiscernible number" of tenants were in arrears.
She said 50% were already in arrears before the policy was brought in.
Housing benefit changes
England, Scotland and Wales
of housing benefit recipients affected by spare room subsidy
28% of those affected have fallen into arrears for the first time
6% of those affected have relocated
3% of those affected have had legal action taken against them, eg evictions
Among the benefits changes introduced on 1 April 2013 was the removal of what ministers called the "spare room subsidy" - social housing tenants deemed to have one spare bedroom have had their housing benefit reduced by 14%. Those with two or more spare bedrooms had reductions of 25%.
There were 498,000 social housing tenants in England, Scotland and Wales who faced having benefits reduced under the policy in November 2013, the Department of Work and Pensions said.
That figure was a reduction of 50,000 from the month after the policy had come into force. It has not been introduced in Northern Ireland.
Labour dubbed the change a "bedroom tax" and has promised to scrap it if it wins the next election.
The government had argued there were two reasons for cutting housing benefit for those of working age living in social housing with spare bedrooms - to reduce the benefits bill and to help the 300,000 people living in overcrowded accommodation.
But the BBC research - involving 331 social housing providers across England, Scotland and Wales with Freedom of Information requests submitted to councils and surveys of housing associations - found just under 6% of tenants whose benefit was cut had moved house.
Ms McVey denied 6% was a failure.
"There has been 30,000 people plus moving in the last 10 or 11 months," she said.
"We were expecting over four or five years for maybe 30% of people to move so it shows really that we are on track."
Kate Webb, head of policy at housing charity Shelter, said one of the reasons stopping people moving was the lack of availability of suitable housing.
She said: "In the short term, the government has to think seriously about whether this is a sensible policy, given that we don't have the smaller homes for people to move in to, and given the levels of hardship and arrears that we are unfortunately going to see building up."
Ms Webb added that many do not see their extra bedrooms as being "spare" rooms, for example if disability equipment is kept in the room or if their children stay at weekends.
"Fundamentally, these are people's homes," she said. "We know that people don't want to move and they will do any other option that will keep a roof over their head for as long as possible."
Prof Rebecca Tunstall, director of the centre for housing policy at the University of York, said: "There were two major aims to this policy - one was to encourage people to move, and the other was to save money for the government in housing benefit payments.
"But those two aims are mutually exclusive. The government has achieved one to a greater extent and the other to a lesser extent."
Asked if the policy had proved successful, she added: "To some extent it's achieved some of its aims. It's achieved an aim of making a saving in housing benefit for national government, probably slightly less than they'd originally hoped for.
"But there are other knock-on costs. There's a social cost for tenants and a cost of having less efficient and fewer new homes. And you can imagine that those costs can start to mount up."
Shadow employment minister Mr Timms said the policy had been a waste of money.
"Eviction is a very costly thing because they will have to be re-housed somewhere at the expense of the state. And that's another reason why it's very likely it's going to end up costing more than it saved," he told the BBC.
"It's been a disaster, it should be scrapped and if this government doesn't scrap it then the next Labour government certainly will."
But Work and Pensions Secretary Iain Duncan Smith said: "It was absolutely necessary that we fixed the broken system which just a year ago allowed the taxpayer to cover the £1m daily cost of spare rooms in social housing.
"We have taken action to help the hundreds of thousands of people living in cramped, overcrowded accommodation and to control the spiralling housing benefit bill, as part of the government's long-term economic plan."