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 the bedroom tax by critics - will free up big homes and save taxpayers £1m a day.
The employment minister said 6% - 30,000 people - was "not a failure".
BBC analysis of the data from social housing providers also suggested 28% of affected tenants were in rent arrears, a year after the changes came in.
But Employment Minister Esther McVey disputed the figures on debt, saying her own feedback from local authorities and the National Housing Federation found an "indiscernible number" of tenants were in arrears.
She said 50% of people affected by the change were already in debt.
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%.
Labour dubbed the change a "bedroom tax" and 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 council and surveys of housing associations - found just under 6% of tenants whose benefit was cut had moved house.
It also found that while most were paying their rent, 28% had fallen into arrears for the first time in the past 12 months.
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.
Affected tenants who had not moved were being forced to make up the shortfall in their income, leading to extra pressure being placed on them to make ends meet, said Prof Tunstall.
"David Cameron's government have pretended this was all about helping people who are overcrowded, but in truth the bedroom tax is a cruel, unfair and appallingly administered policy."
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.