Media playback is unsupported on your device Media caption Marion Smith and her family have been told it will be "decades" before they can move to a big enough house

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 11% 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 PA

Media playback is unsupported on your device Media caption Employment minister Esther McVey: Housing benefits scheme "on track"

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%.

Analysis This research suggests the government is on course to meet a key target, namely to cut the overall housing benefit bill. Few people moving means more people contributing to their own rent. But doing so it seems will come at the cost of another goal - cutting overcrowding. Many simply can't move, repeatedly failing to find smaller properties. With demand for new homes constantly outstripping supply, too many families are likely to stay in crowded, unhealthy households. The increase in rent arrears is not only a problem for those tenants unable to pay. While it could lead to evictions and heartache, it is also likely to cause problems for councils and housing associations. Not only will their debts increase but their ability to invest in new homes will also be reduced. Given they're the main builders of affordable homes, it will be unfortunate if a policy intended to cut overcrowding leads to fewer homes being built.

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.

'On track'

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 feel trapped' Marion Smith lives in a two-bedroom apartment in Dyce, Aberdeen, with her husband Mark and their three children. They are currently 36th in line for a new property in the area. "It can be quite claustrophobic staying here," said Mrs Smith. "We feel kind of trapped in our situation at the moment, so that impacts on us. "The children are all in one room, so it can be stressful for them. They don't get any space away from each other. Our oldest child is eight and she's at the stage where she's needing a bit of space now and hasn't got the same interests as my youngest child, who's four." The family had hoped the benefit changes would result in more properties being freed up. "It's not fair for people like us at the moment," Mrs Smith said. With one property available each year in her area, Mrs Smith said her family faced waiting for "decades". "Realistically, we're going to have to wait until I'm in full-time employment and can start saving for a deposit and can buy somewhere," she said. "We've accepted that, although it's depressing."

"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."

'Costly'

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.

'I had no choice' When the changes came into force, Jayne Dennis was one of those who moved from her three-bedroom home. Ms Dennis said her children had moved out and she was then under-occupying by two rooms, with a cut to her benefits of £12 per room. "With that really, I had no choice but to move," she said. In her old home, she started to build up arrears. "I was finding it difficult to pay that," she said. "You've got your other bills at the same time. You don't pay it all, you pay like half of it, because you haven't got the money." She said her old home had been vacant for three months. She said. "You'd think they'd have filled it by now, but no. I think it's because we're out of the way and a lot of people don't like to be out of the way."

"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."