MPs are to be asked to throw out restrictions to the Government's proposed "bedroom tax" in the latest round of parliamentary wrangling over Iain Duncan Smith's welfare shake-up.

The Government suffered a setback in the House of Lords last week over the plans, which will dock benefits for tenants in social housing with spare rooms.

A rebellion by six Liberal Democrat peers helped inflict a narrow defeat on ministers over the change, meaning the disabled, war widows and foster carers would not be affected unless they refused to take up an offer of a suitable alternative home.

Peers voted by a majority 10 in favour of an amendment to the Welfare Reform Bill by crossbencher Lord Best.

He warned that families on low incomes hit by the size criteria, which would see a 14% reduction in housing benefits for having a spare room or a 25% reduction for having more than one extra bedroom, could be forced to use payday lenders or loan sharks to make up the shortfall when the changes come into force next April. "While older tenants may have put aside a bit, few will be able to cope when faced with a new tax of £728 every year on top of the rises in their heating bills and other costs," he said.

But MPs will be asked to overturn the defeat in the latest stage of the "ping pong" process, which has seen the Bill sent back and forth between the two Houses of Parliament as the Lords and Commons search for an agreement over the proposals.

The size criteria is the final issue on which the two chambers are still in dispute. The Welfare Reform Bill puts in place a £26,000 benefits cap and introduces a new, simplified universal credit to replace a complex range of payments.

Earlier this month MPs overturned a series of defeats suffered by the Government in the Lords and, because the measures would have involved extra spending, the changes were ruled to have infringed on the "financial privilege" of the Commons, which has responsibility for the budget.

The ruling was fiercely challenged by some senior peers, who argued it had restricted their ability to scrutinise the legislation. The £100 million cost of Lord Best's measure means financial privilege could again be used as the reason if MPs delete the amendment.

A Department of Work and Pensions spokesman said: "The House of Commons has made its position clear on amendments which would result in additional spending, and the Government will seek to overturn the size criteria amendment when the Bill returns for further consideration by the Commons. The majority of the public agree with the Government's welfare reforms and we look forward to delivering on these radical proposals that will make our welfare system better and fairer."