Theresa May’s Brexit stance has come under concerted attack from within her party, with senior Tories lining up to warn against making fresh concessions to Brussels as negotiations reach their final, frantic stage.

Ministers have been told to expect extensive discussions of Brexit at next week’s cabinet meeting; and with some preferring a looser, Canada-style deal to May’s Chequers plan, pressure is mounting on Downing Street to change course.

The Brexit secretary, Dominic Raab, defended the government’s strategy robustly in the House of Commons on Tuesday, insisting the UK and Brussels were closing in on “workable solutions” to the outstanding issues.

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“These negotiations were always going to be tough in the final stretch. That’s all the more reason why we must hold our nerve, stay resolute and focused. I’m confident we’ll reach a deal this autumn,” he said.

But his remarks were ridiculed by Keir Starmer, the shadow Brexit secretary, who said: “We’ve been here before, many times ... It’s like Groundhog Day. We get the same old story. The secretary of state pretends everything is going according to plan.”

Earlier, Penny Mordaunt, a leading cabinet Brexiter, refused to explicitly back May’s Chequers plan, simply saying she would not give a “running commentary” on the proposals.

While she insisted May had her support for now, the international aid secretary raised the possibility that this could be conditional if the final deal looked like an “attempt to derail or fudge” the outcome of the Brexit vote.

“The prime minister can count on my support. But what I would say is that we don’t know where this is going to end up. We are at a critical moment now. The ball is firmly back in the EU’s court; we are waiting for them to respond,” she said.

Facebook Twitter Pinterest Penny Mordaunt refused to explicitly back May’s Chequers plan. Photograph: Jack Taylor/Getty Images

David Davis, who resigned as Brexit secretary after the Chequers summit, has written to every Conservative MP warning that remaining on the current course, which envisages a “common rulebook” for goods, would have dire consequences at the ballot box.

“If we stay on our current trajectory we will go into the next election with the government having delivered none of the benefits of Brexit, with the country reduced to being a rule-taker from Brussels, and having failed to deal with a number of promises in the manifesto and the Lancaster House speech,” he said.

Davis’s pointed intervention was one of several by prominent party figures on Tuesday. One senior Brexiter said: “It’s part of a carefully calibrated and timed campaign and there is more to come.”

Mark Harper, a former chief whip who is broadly supportive of May, added his name to those who believe a looser, Canada-style trade relationship would have a better chance of getting through the Commons.

Harper said he had been alarmed by reports that Tory whips were relying on winning over Labour MPs to their cause when the government brings a Brexit deal back to parliament.

“I would prefer the prime minister to come back with a deal that wins over the Conservative party, which means she can be confident she’ll get it through,” he said. “She needs to have her own team behind her.”

He said May’s position would inevitably evolve as negotiations progressed – but it should be towards a looser, Canada-style trade deal, not a closer, Norway-type relationship.

“I think there’s a place she could get to where she could pretty much get every single Conservative MP onside,” he said.

Steve Baker, Davis’s former colleague at the Department for Exiting the EU, also criticised the Chequers approach – and claimed 40 of his colleagues were determined to vote against it, whatever the consequences.

In the Commons, Raab rejected calls from Brexiters for May to dump her Chequers plan and go for a Canada-style agreement instead. He told Baker his free trade proposal would be “a shortcut to no deal”.

“While it is theoretically possible for us to do that, we can’t do it and have a deal with the EU,” he said, pointing out that Brussels had insisted on a legally binding backstop to the Irish border issue that would in reality make a free trade deal impossible.

Raab also denied the government was preparing to accept the whole of the UK effectively remaining in a customs union indefinitely, as a way of avoiding a hard border in Ireland. Pressed on the issue by MPs, he said any extension of a customs union would have to be “temporary, limited and finite”.

The deputy leader of the Democratic Unionist party, Nigel Dodds, angrily warned the government against any deal that would separate Northern Ireland from the rest of the UK. “We’ve been clear about that from day one. It’s why we had the debacle [over the backstop] in December. Let’s not repeat that mistake.”

Last week, May warned her colleagues at the party conference in Birmingham: “If we all go off in different directions in pursuit of our own visions of the perfect Brexit, we risk ending up with no Brexit at all.”

With intensive talks taking place in Brussels all week, backbench MPs critical of May’s approach are making their views known. Brexiters inside May’s cabinet are also watching developments closely.

Those calling on May to “chuck Chequers” are concerned that the “common rulebook” will mean too much alignment with EU rules, and frictionless trade for goods will restrict the UK’s ability to strike future trade deals.