The Government has offered concessions over its £26,000 cap on benefits as MPs threw out changes to the controversial welfare reforms made in the House of Lords.
Once the changes come into force in April 2013, people who lose their job will be given a nine-month grace period to find work before the cap is imposed, employment minister Chris Grayling said.
Workless families currently receiving payments at a level above the cap will be given support to make them understand the need to find jobs before the April 2013 deadline.
At Prime Minister's Question Time David Cameron challenged Labour to support the threshold, saying: "The cap is right and the cap is fair."
A Lords amendment, which was led by Church of England bishops and removed child benefit from the cap, was overturned by 334 votes to 251, majority 83.
Mr Grayling said the public "overwhelmingly" supported the Government's stance to introduce a benefits cap at £26,000 a year, equivalent to a gross salary of £35,000.
He said Labour had been guilty of "flip-flopping" on the issue, initially supporting a benefits ceiling before the party's peers supported an amendment in the Lords to exclude child benefit from any cap.
But in the face of concerns from Lib Dem deputy leader Simon Hughes (Bermondsey and Old Southwark) and Tory MP Mark Field (Cities of London and Westminster), who said they were worried families in the capital might have to move out because of the changes, Mr Grayling announced a number of concessions.
He said families would receive a 12-month grace period to find work, while those who lose their job through no fault of their own after being employed for a year would be given nine months in which to find new employment.
Meanwhile, households entitled to working tax credit would be exempted from the cap along with working households on universal credit after 2013.
War widows and widowers would also be exempted while households receiving the support component of employment and support allowance (ESA) but not receiving disability living allowance would also not be penalised, he said.
"Excluding child benefit will only dilute our aim that being in work must always pay better than relying on benefits alone," Mr Grayling told MPs.
"The fact is that the arguments in favour of a cap are in terms of fairness, ending a situation where for some people benefit rates are so high that it is not worth working. It is worth saying that this is an issue where the public of this country are overwhelmingly behind us."
Setting out Labour's position, shadow work and pensions secretary Liam Byrne said: "We are in favour of a benefit cap, but we like a cap that doesn't backfire."
Earlier MPs reversed a series of changes to the ESA made in the Lords.
The measures will go back to the Lords, but because it was decided that they involved spending commitments the Commons claimed "financial privilege" as its reason for overturning the amendments made by peers - effectively preventing peers making further changes.
Lord Hunt of Kings Heath, the deputy leader of Labour peers, said ministers were "hiding behind parliamentary procedure to curtail consideration of the amendments that we passed".
Tory former cabinet minister Lord Mackay of Clashfern, who led the biggest Lords rebellion, said it was a "waste of taxpayers' money at a time of considerable austerity" for peers to pass amendments that were subsequently rejected out of hand.
As MPs overturned the Lords' amendments to the Welfare Reform Bill, Mr Grayling said: "We have to change the nature of our welfare state.
"We have got to move away from the world which existed under the previous government, where children grew up generation after generation in houses where no one worked, entire communities had people who had no experience of work in their family, who knew nothing about how to improve their lot in life."
He said the revamp would "transform our welfare state" and accused Labour of "just not getting it" and "dancing around the edges".
The Government suffered a series of defeats over the ESA measures in the Welfare Reform Bill in the Lords, but comfortably overturned them in the Commons.
The Bill as now drafted means people who are recovering from an illness or injury can get contributory ESA for one year, half the period that the Lords decided.
The limit would also apply to cancer patients, despite moves by peers to exempt sufferers from the time limit.
On the amendment lifting the time limit on contributory ESA, MPs voted to make the limit one year by 332 to 266, a majority of 66.
The amendment exempting cancer patients from the time limit was overturned by 328 to 265, a majority of 63.
An amendment which would have allowed the Lords to stop changes to the youth element of ESA was defeated by 324 to 266, a majority of 58.