Cabinet ministers including Philip Hammond and Greg Clark ramped up their opposition to a no-deal Brexit on Thursday, as Theresa May convened a meeting in Downing Street with ministers panicked about the extent of the parliamentary rebellion against her plan.

Soft Brexiters such as Hammond, the chancellor, Clark, the business secretary, and David Gauke, the justice secretary, have expressed serious alarm about the mounting prospect of no deal if the vote falls next Tuesday.

“Greg and David in particular have made it clear they could not countenance it,” one cabinet source said.

Hammond and Gauke were among the ministers who attended the afternoon meeting in No 10 on Thursday, as well as the chief whip, Julian Smith, and May’s de facto deputy, David Lidington and Brexiters Andrea Leadsom, Liam Fox and Michael Gove, among others.

Downing Street sources described the meeting as informal, without an agenda, though ministers discussed pressure to pull Tuesday’s vote.

One cabinet source described it as a meeting to “take stock” of the difficult situation in parliament. Another expressed frustration that there seemed to be nothing that concerned ministers could say to prompt an honest examination of the state of play by May.

May has resisted calls to delay the vote in the face of near-certain defeat. Sir Graham Brady, who chairs the 1922 Committee of Tory backbenchers, is among those who have urged the prime minister to re-think the timing.

More than 100 Tory MPs have publicly stated they will vote against May’s deal, a number which is growing rather than falling as the day draws nearer.

The cabinet’s soft Brexit faction has become increasingly convinced that a so-called “Norway plus” option that keeps the UK in the European Economic Area and a customs union may be the only route to command a majority in parliament, several sources said, a view promoted by the former cabinet minister Sir Oliver Letwin.

One cabinet minister said it had been underestimated how instrumental the amendment put down by Dominic Grieve had been. This gives parliament the chance to vote on amendments to a government statement should the deal be voted down.

If any parliamentary faction can command a majority to pass their version of Brexit as an amendment, “that is effectively the government”, the cabinet minister believes.

May would be highly unlikely to deliver a Norway-style option herself – her opposition to free movement is described by No 10 insiders as her “reddest of red lines”.

Corbyn urges support for his Brexit plan as Commons vote nears Read more

On Thursday, both Hammond and Clark warned in stark terms about the damaging impact of no deal.

Clark, speaking on a visit to Bristol, said: “It would be crazy, just at a time of the prospect of great prosperity, to introduce not just obstacles but to really destroy the foundations of the success of some of our most brilliant industries.”

Speaking in the Commons to open the third day of the Brexit debates, Hammond said the consequences of no deal were “too awful to contemplate”, warning that car manufacturers would face tariffs of 10% and agricultural tariffs would be even higher.

“I’ve heard that we have nothing to fear from no deal, nothing except a cliff-edge Brexit in just four months’ time,” he said, adding that it would also mean “the end of frictionless trade with our biggest export market, restrictions on our citizens travelling in Europe, nothing except being the only developed economy in the world trading with the EU on purely WTO terms”.

The chancellor said it was “simply a delusion” that the deal could be renegotiated. “I have observed this process at close quarters for two-and-a-half years and I’m absolutely clear about one thing – this deal is the best deal to exit the EU that is available or that is going to be available,” he said.

An intervention to try to win over rebellious Tories concerned about the backstop came late on Thursday night. Hugo Swire, Richard Graham and Bob Neill tabled an amendment to the motion aiming to give MPs more power over the handling of the backstop designed to avoid a hard border between Northern Ireland and the Republic of Ireland.

The amendment, which has the hallmarks of having tacit government approval, gives MPs power to direct the government’s approach as to whether to enter backstop arrangements or extend the transition. May had made a similar offer earlier in the day.

The amendment also requires the prime minister to report back to parliament by March 2020 on the status of negotiations, and says the government should have “a duty” to have alternative arrangements in place after one year of the backstop coming into force.

The DUP’s leader, Arlene Foster, denounced the proposed compromise within an hour of publication, saying “domestic legislative tinkering won’t cut it”. There are also questions as to whether new limitations on the backstop’s effectiveness would be acceptable to the EU.

May and Smith have insisted there is no prospect of Downing Street cancelling the Brexit vote next Tuesday. “The plan is to deliver the vote on Tuesday,” a cabinet source said after the meeting, adding that the prospect “looks difficult but that is the plan”.

Smith said there would not be any delay but admitted it was an “uphill challenge” to convince his mutinous colleagues. “There is no plan for a vote loss,” he told ITV.

Former Brexit secretary David Davis called on MPs to vote down the deal in such numbers that it cannot be revived. Davis told the House magazine that MPs must “make sure the stake goes through its heart and it gets buried at the crossroads” by the size of the revolt.

“She’ll look at the size of the rebellion,” he said. “She’ll also look at what’s said by key players and try to segment it to see whether or not there’s a coalition she can build to still deliver something like what she’s got.”

On Friday more than 30 ministers, including many from the cabinet, will be dispatched across the UK to sell the deal.

The Brexit secretary, Stephen Barclay, will be in heavily leave-voting Peterborough and Hammond will visit a school in Chertsey in Surrey. Liz Truss, the chief secretary to the Treasury, will be in East Anglia visiting a butcher.