Church of England bishops were among those who voted against government plans to put a £26,000 cap on the amount of benefits UK adults can receive.

On Monday, the House of Lords voted on the plans, which would limit the amount of benefits available to £500 a week for families, or £350 for childless single-adult homes.

But the government's proposals were defeated as members supported an amendment by Rt Rev John Packer, the Bishop of Ripon and Leeds, which would exclude child benefits from the annual cap.

Former Liberal Democrat leader Lord Ashdown had called the proposals "completely unacceptable", joining bishops and other rebel Lib Dems in their criticism of the proposals contained in the welfare reform bill.

Ministers claim that introducing the benefits cap would save around £51 million over three years, which could help cut the country's deficit. It would also encourage those who are able to go out to work rather than claim benefits.

But the bishops claimed that the cap could lead to a rise in homelessness and child poverty. But refuting the claims on BBC Radio Four's Today programme on Monday, Iain Duncan Smith, the work and pensions secretary, said: "I just wish they'd call us to get their figures right."

Mr Duncan Smith has been backed by both the prime minister and the deputy prime minister in the plans. David Cameron told The Telegraph: "It's a basic issue of fairness. Should people really be able to earn more than £26,000 just through benefits alone?

"I don't believe they should. And I think the overwhelming majority of people in the country would back that view."

The Children's Society welcomed the result of the vote, with Enver Solomon, its policy director, saying: "The Lords have stood up to the government and sent a clear message in support of children up and down the country.

"The Children's Society is delighted that the Lords have seen sense today and excluded child benefit when calculating the benefit cap. Children should not be held responsible and penalised for the employment circumstances of their parents.

"If the intention of the benefit cap is to promote fairness, it is totally unfair that a small family with a household income of £80,000 a year receive it, yet a large family with a benefit income of £26,000 are excluded."

The Centre for Social Justice was, however, disappointed by the result. Gavin Poole, executive director, said: "The plans to cap benefits at £26,000 a year are part of a wider package of reforms which will help bring to an end our damaging welfare dependency culture.

"This result is peculiarly out of line with public opinion which shows that almost 80 per cent were in support of the proposed cap.

"Britain has been gripped by a worklessness crisis for years - the number of households where no-one has ever worked doubled since 1997 and two million children are growing up in workless households. Tonight members of the House of Lords failed to provide the leadership required to start reversing that failure.

"We urge the government to press ahead with its benefit cap reforms whilst ensuring the families negatively impacted by it in the short term will get the help they require."

Dave Landrum, director of advocacy at the Evangelical Alliance, said: "As the state looks to spend less over the next few years, the dilemma thrown up in the debate over the cap on welfare represents a challenge to us all. How do we balance the need for an incentive to work with a responsibility to our poorest families? In addressing this question, we need to remind our politicians that there must be an accompanying focus on the obscene and increasing levels of income inequality that plagues our society."