Labour has stepped up its protests against housing benefit cuts - claiming there is no alternative local accommodation for 96% of those hit by the so-called "bedroom tax".
The controversial move to withdraw benefit from social housing tenants deemed to have a spare room comes into force today as part of a package of welfare reforms.
Those with one spare room will be deducted 14% and those with more lose a quarter - removing what the Government calls a "spare room subsidy" not available to private tenants.
Ministers say the change - affecting around 660,000 claimants - will save the taxpayer £500 million a year and free up unused space for people on waiting lists.
But they have been forced to make concessions to protect foster parents and armed forces families and face a legal challenge on behalf of disabled children.
Labour said freedom of information responses showed local councils had sufficient one and two bedroom properties to house only one in 20 of those families with spare rooms.
Responses from 37 authorities across Britain revealed 96,041 households faced losing benefit but there were only 3,688 smaller homes available.
Shadow work and pensions secretary Liam Byrne said: "These shocking new figures reveal the big lie behind this Government's cruel bedroom tax.
"They say it's not a tax but 96% of people have nowhere to move to.
"In the same week that millionaires get a huge tax cut, hundreds of thousands of vulnerable people will be hit by a vicious tax they can't escape.
"This wicked bedroom tax is going to rip neighbour from neighbour, force vulnerable people to food banks and loan sharks, and end up costing Britain more than it saves as tenants are forced to go homeless or move into the expensive private rented sector.
"It is the worst possible blend of cruelty and incompetence. The Government must think again and drop this tax now."
The National Housing Federation (NHF) says the reform will fail to solve overcrowding and could even increase the welfare bill.
If everyone moved, many would end up in the private rented sector, in some cases meaning larger housing benefit claims and the expense of adapting new homes for disabled tenants.
It found around two-thirds of those affected are disabled. The Government has said local councils have been provided with sufficient hardship funds to deal with such cases.
Disabled children expected to share a room under the new rules are among a group who have won the right to a judicial review of the policy, claiming it affects them disproportionately.