After proposing a £26k cap on benefits at a conference last year, the Conservatives have now backed down and will allow the cap to be relaxed in "exceptional circumstances".
Welfare reform minister Lord Freud said that while in most cases the amount that a household will be allowed to receive each year in benefits will be capped at £26,000 (the average yearly earnings of a working family), for some larger families there may be exemptions.
Other exemptions include "if you are in work, you are not affected. Secondly if you're a disabled person or there's a disabled person in the household, you're not affected. If you're a war widow or a widower, you're not affected."
The cap, which comes into action in 2013, will be applied in part by reducing housing benefit and will have an effect on about 50,000 families. Most of these families consist of single mothers with more than five children.
Jenny Willott, who co-chairs the Lib Dem backbench committee on Welfare reform, said: "We do need to make sure that those larger families, where there are exceptional circumstances, get the benefits that they need, rather than it being capped too low and they don't have enough to pay for the daily costs of living or even to pay enough for their housing."
There are 100,000 benefit claimants who have families with four children or more, and more than 900 families with more than eight children.
Lord Freud has allowed that in some of these cases, a cap on benefits would be unfair, despite critics pointing out that the cap was introduced to combat cases where large out-of-work families were receiving more than £100,000 a year in benefits.
But Prime Minister David Cameron has claimed that he is still committed to the benefits cap plans as he understands that many working families find it unfair that taxpayers should support those who have children they cannot afford.
The Department for Works and Pensions said: "The point of the benefit cap is to set a limit as to what people can expect from the system when they are not working.
"The Government believes it is not fair that people who are in work can earn less than those who are on benefits."
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