Families affected by the government's £26,000 welfare cap will be given at least nine months to adapt to the loss of benefits, under concessions to be outlined by the Government.
A discretionary fund will also be available to local authorities to ease difficult cases, and ensure families are not forced to move during critical points in a child's schooling.
The moves are likely to be announced by Iain Duncan Smith, the Work and Pensions Secretary, when the controversial Welfare Reform Bill returns to be debated in the House of Commons today.
Government sources say ministers will seek to overturn seven major amendments to the bill imposed by the Lords in successive rebellions over the past fortnight, including a revolt on Tuesday, when peers voted by 246-230 against plans to cut payments worth up to £1,400 to families with disabled children.
They hope the concessions – which could also include an exemption for the lowest-earning single parents against proposed fees for using the Child Support Agency – will be enough to buy off rebel Liberal Democrats who helped inflict defeat on the Government in the Lords.
It has been suggested that as many as 200,000 people on housing benefits will have to move from areas of high rents as a result of the change. The government says the actual figure is 67,000. That number, it is claimed, will be reduced if the cap is not imposed as soon as benefits are claimed, or when the claimant is forced into expensive temporary accommodation.