Labour has said it will reverse controversial changes to housing benefit if it wins the next election.
Ed Miliband said the cut affecting social tenants in England, Scotland and Wales deemed to have spare bedrooms was unfair. Labour aims to fund its change by blocking tax cuts for businesses.
Critics called the cut a "bedroom tax".
The government argues it ends "spare room subsidies" unavailable in the private sector, and that the £23bn-a-year housing benefit bill must be cut.
The announcement comes with the Labour Party conference about to start in Brighton.
Since April, social housing tenants deemed to have spare rooms have either had to pay more in rent or move somewhere smaller.
For months Labour has argued the change is wrong, unfair and penalises disabled people in particular, but had not committed itself to reverse the policy if it was in power after the election.
But Mr Miliband has now said the change would be paid for by scrapping a tax break for hedge funds and the Treasury's new shares-for-rights scheme.
The Labour leader said the benefit change was "wrong, iniquitous and was not working". He told the BBC that two-thirds of those affected were disabled and would struggle to find anywhere else to live.
"We are serving notice that we will end the 'bedroom tax'," he said.
He said the "costed and credible" commitment was a "symbol of what a Labour government would do and the difference a Labour government would make".
The BBC's political correspondent Ben Wright said the move would cheer Labour's rank-and-file and please critics within the party who say it urgently needs clear policies.
But the Treasury claims Labour's figures fail to add up and that it would fund the changes by a tax on pensions and more borrowing.
"Labour's first policy commitment, after three years of waiting, is more spending on housing benefit, funded by a tax on pensions and more borrowing," said Treasury Minister Sajid Javid.
"Despite promising 'discipline' on borrowing, Ed Miliband has shown he is too weak to deliver."
Business minister Matthew Hancock said that reversing the housing benefit change would "damage the UK economy and it would lead to higher taxes and higher mortgage rates".
The government insists the housing benefit bill must come down, and will press Labour to explain how it will do that.
A Department for Work and Pensions spokeswoman said there were 250,000 households in overcrowded social homes, and that the housing benefit change would help "make better use of our housing stock".
She said: "Reforms mean families receive help for the number of bedrooms they need, and these are exactly same rules as in the private sector."
On Thursday, the TUC reported that one in three council tenants affected by the cut had fallen behind in their rent since the policy's introduction.
National Housing Federation chief executive David Orr said the policy was "an unfair, ill-planned disaster that is hurting our poorest families".
"There is no other option but to repeal," he said.
Earlier this month, UN official Raquel Rolnik, who is producing a report on adequate housing around the world, called for the policy to be suspended to allow time to assess its human rights implications.
She said that, based on hundreds of testimonies, the measure seemed to have been designed "without the human component in mind".
She was accused of showing "political bias" by Conservative chairman Grant Shapps, who added that he was writing to the UN secretary general to complain.