Jo Johnson, the Conservative MP who resigned as a minister to back a second Brexit referendum, will on Monday throw his weight behind a bid to force the government to publish economic forecasts that compare its deal with remaining in the European Union.

The Orpington MP is expected to make his first speech from the backbenches to support a cross-party amendment to the finance bill. Tabled by Labour’s Chuka Umunna and the Conservative Anna Soubry, the amendment is backed by 70 MPs from six parties, including the Liberal Democrat leader, Vince Cable, and the SNP’s Europe spokesman, Stephen Gethins.

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It is aimed at forcing the Treasury to publish projections comparing the “fiscal and economic effects” of the government’s Brexit deal, with the outlook “If the United Kingdom had remained a member of the European Union”.

Johnson is one of 11 Conservative MPs who have signed the amendment, more than enough to overturn the prime minister’s majority if, as expected, Labour supports it.

One of the Tory signatories, Ken Clarke, said: “The only way to prevent the current shambles from becoming a serious national crisis will be for parliament to exercise a well-informed and sensible judgment in the national interest when it votes on all the key issues. The procedures of the House of Commons must be followed in order to protect the national interest from any attempts to confine parliamentary sovereignty.”

The government has committed to publishing a range of analysis to aid MPs as they weigh up whether to support Theresa May’s Brexit deal in a “meaningful vote” when she brings it back to parliament, expected to be early next month.

But it is not planning to produce an assessment of the impact of the UK remaining an EU member state. The amendment would force it to do so – and allow the analysis to be checked by the independent Office for Budget Responsibility.

Umunna, the MP for Streatham, who is campaigning vigorously for a fresh Brexit referendum, said: “The prime minister told the House of Commons last week that the country faces three choices – no Brexit, no deal and her agreement – and therefore it is only right that MPs are provided with an economic analysis with a comparison between those options. Anything less would amount to pulling the wool over the eyes of parliamentarians and the people we represent.”

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Under the Fixed-term Parliaments Act, a defeat on the finance bill, which implements the budget, is no longer formally considered a matter of no confidence that would cause the government to fall.

But Downing Street has previously opted to cave in on contentious issues where it risks parliamentary defeat. It has already been forced to reverse plans in the finance bill to delay cutting the stakes on controversial FOBT gambling machines. The issue led to the resignation of the sports minister Tracey Crouch before the government executed an embarrassing U-turn last week in the face of opposition on its own benches.

Johnson resigned from the government earlier this month, four months after his Brexiter brother, Boris. In his resignation letter, he said: “To present the nation with a choice between two deeply unattractive outcomes, vassalage and chaos, is a failure of British statecraft on a scale unseen since the Suez crisis.”