The House of Lords dealt the Government's welfare reforms another major blow as it threw out plans to charge single parents for using the Child Support Agency.

In the sixth Lords defeat for Iain Duncan Smith's benefits shake-up, Conservatives and Liberal Democrats joined Labour peers to vote by a majority of 142 against the move last night.

The Department for Work and Pensions said it would seek to overturn the latest amendment to the Welfare Reform Bill when it returned to the Commons.

Last night's rebellion, on the final day of the Bill's stormy report stage in the Lords, was led by Tory former lord chancellor Lord Mackay of Clashfern.

Lord Mackay said the Government's plans could have the effect of putting single mothers off seeking the financial support they were entitled to.

He said: "The motivation for these charges is said by the Government to be to bring people to voluntary agreement.

"I am entirely in favour of that but if that proves impossible where the woman is at the stage where there is nothing more she can do, the only thing she can do is pay."

Lord Mackay's amendment would stop an upfront charge of £100 or £50 plus a levy of up to 12% on maintenance payments applying if a single parent, generally a mother, had taken "reasonable" steps to get the other parent to come to a voluntary agreement on child support.

Gingerbread, which supports one parent families, urged the Government to rethink its reforms in the wake of the defeat.

Chief executive Fiona Weir said: "The Lords have sent a very strong message to the Government that there is widespread concern about its plans to charge parents with care to use the Child Support Agency.

"We hope Government will now rethink these proposals before it goes back to the Commons."

But a spokeswoman for the Department for Work and Pensions said: "We are disappointed that the Lords seem content to leave in place a system that has consistently failed children and we will seek to overturn this in the House of Commons.

"The fact is that child maintenance needs to be reformed because it does not work.

"Our reforms would see a doubling of support for families going through a break-up to come to their own financial arrangements with a far improved statutory scheme in place for those that really need it.

"It is right and fair that there is a charge for using a service that can cost the taxpayer around £25,000 per case and almost half a billion pounds per year."

The coalition Government had already suffered five defeats on the Bill before last night's setback.

The most prominent was on Monday when peers voted to exempt child benefit from the Work and Pensions Secretary Mr Duncan Smith's planned £26,000-a-year cap on household benefits.

Downing Street insisted that the reforms had public support.

A spokeswoman said: "We believe they have the backing of the public. These are the changes that people want, to make our welfare fairer."

Labour also urged the Government to "think again".

Shadow work and pensions secretary Liam Byrne said yesterday: "The Government should never have proposed we make it harder for mums trying to raise a family on their own to get the help they are entitled to from absent fathers.

"They have got this comprehensively wrong. I really hope tonight's comprehensive defeat will now force the Government to think again."