Iain Duncan Smith has pledged to overturn the House of Lords' amendments to his Welfare Reform Bill, including the vote to cancel charges for single parents to use the Child Support Agency (CSA).

On Wednesday peers delivered their largest-ever defeat on the coalition by voting by a majority of 142 to cancel plans to introduce CSA charges. The amendment was tabled by Lord Mackay, a Conservative peer, and backed by many former Tory ministers including Lord Howe and Lord Lawson.

But the work and pensions secretary told Andrew Marr on Sunday morning that the current system led to parents being "almost forced to be at each other's throats," arguing that the charges would lead to disputes over child maintenance being settled out of courts more often.

"If you have a relatively small charge, what happens is that people will think about it," said Duncan Smith, insisting that the proposals would be "better for the children."

On Wednesday MPs will consider all the amendments made by the Lords to the Welfare Reform Bill, and the secretary of state confirmed that coalition MPs would be whipped into overturning them. Most of the amendments were passed by relatively small margins, but the CSA amendment was overwhelmingly passed. This raises the prospect of "parliamentary ping-pong" taking place between the two houses in the coming days.

On the CSA charges, IDS claimed: "We want to make sure that this is a balance. We're not asking for much, It's only about 9%. We're going to pick up the lion share of the cost."

He was particularly bullish on the planned benefit cap of £26,000 per household. An amendment by peers would make child benefit exempt from this calculation, but IDS insisted it would also be overturned.

"Even among Labour and Liberal voters... it's overwhelmingly popular," he said. "Why should someone on benefits earn more than the average wage?

"We have people living in London that cost over £100,000 a year to rent... that's the kind of nonsense that we've got into."

The government has a majority of more than 80 in the House of Commons, but lacks a concrete majority in the Lords. In the unelected chamber it requires the support of at least some of the independent cross-bench MPs.

Nick Clegg wants to replace the Lords with a mostly elected chamber, although the Bishops which introduced one of the amendements last week would be retained under the deputy prime minister's draft proposals.

If the Commons and the Lords cannot agree, there will be a state of "ping-pong" when the Lords will be urged to accept the will of the elected lower chamber. The government may use the Parliament Act - the equivalent of a veto by the Commons, if there is no agreement, but that could delay Iain Duncan Smith's welfare reforms for months.