David Cameron faces a backlash over welfare in the House of Lords after Labour and Liberal Democrat peers tabled motions to block cuts to tax credits.

In a move the prime minister said overstepped their constitutional right to challenge the central financial decision of the Commons, Lib Dem peers said they had tabled a fatal motion that would require the government to start persuading parliament to endorse £4.4bn tax credits cuts starting next April.

The Labour backbencher Baroness Hollis tabled a motion that withholds endorsement for the cuts until the government produces a scheme that protects all existing tax credit claimants for at least three years. A third motion may also be tabled by cross bencher Baroness Meacher, which may also delay the cuts.

With only 249 Conservative peers in an 808 strong upper house, Cameron faces the real prospect of defeat on one of the votes, as long as the cross benchers, who are inclined to respect the limits of the powers of the Lords, decide not to swing behind the government on a point of constitutional principle.

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Government sources claimed the Hollis amendment was just as constitutionally improper as the Liberal democrat “fatal amendment”, saying: “These amendments amount to the same thing if passed: they would mean the House of Lords blocking the government’s policy on tax credits and holding the government hostage.

“The tax credits regulations would not stand approved if either was accepted. And the House of Lords would have done that on an issue exclusively about public spending and taxation.”

The Commons Speaker, John Bercow, sent a coded warning to the Lords not to overreach itself by blocking the government’s tax credits cuts. “The constitutional position is clear and longstanding, he said. “The Lords can look after itself, but we also can and will look after ourselves”.

Adding that he did not want to see a public confrontation between the two houses, he said: “In the final analysis, each House knows what the factual constitutional position is and that position is what it is of longstanding.”

It is traditionally understood that the unelected peers in the House of Lords should not revise the major financial decisions of the Commons. But Labour claims the measure was not in the Conservative manifesto, and that statutory instrument – the method George Osborne, the chancellor, has chosen to implement the cuts – has been challenged in the past.

Cameron was challenged by Jeremy Corbyn during prime minister’s questions to admit he had broken a solemn promise to voters in the general election that he had no plans to cut tax credits.

The prime minister responded by recalling his promise to cut £12bn from the welfare bill at the election, and said he was “delighted” that the changes had been passed by MPs on Tuesday night. Labour MPs said his use of the word “delight” may come back to haunt him.

Cameron, responding to a question posed by Tory backbencher Jacob Rees-Mogg, warned the Lords not to block the measure when it goes before peers on Monday. “This house has now decided twice in favour of this measure, once voting on the SI [statutory instrument], again last night … I think the House of Lords should listen to that very carefully and take note that it’s for this house to make financial decisions,” he said.

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Rees-Mogg referred to the 1911 Parliament Act, bought in by the Liberal government to prevent the House of Lords rebuffing money bills after the Tory-led Lords rejected the “People’s Budget”. Cameron said: “Clearly under that act, it’s supposed to be that issues of finance are decided in this House.”

He added: “The tax credit changes are part of a package, a package that includes a higher national living wage and tax reductions. I think that is the right approach for our country – let’s make work pay, let’s allow people to earn more, let’s cut their taxes and let’s make welfare affordable.”

Cameron faces at least four further challenges beyond the Lords vote on Monday. The work and pensions select committee is to hold an evidence session from leading experts from the Institute for Fiscal Studies and Resolution Foundation that is intended to set out the scale of the impact on the tax credit cuts, especially among those in work.

The Resolution Foundation is due to produce alternative proposals early in November at an event attended by Conservative writer Tim Montgomerie and Frank Field, the Labour chairman of the work and pensions selection committee.

The chairman of the government’s independent social security advisory committee, Paul Gray, said ministers had still not set out the full impact of the tax credit cuts nor explained what it means for universal credit, despite sending a letter on 9 September asking for more details.

MPs are to debate a cross-party supported motion next Thursday that will urge the government to mitigate the impact of the cuts. Ministers are entitled to ignore such backbench-tabled Commons motions, but it would be embarrassing to see large numbers of Conservatives urging Osborne to reconsider.

In a joint statement, Field and the Conservative backbencher David Davis said Thursday’s debate would be a chance to consider the issue on a cross-party basis. They said: “All the MPs requesting the debate wish to have a motion which is designed to help the government meet its fiscal goals while supporting some of our most vulnerable constituents.”