Hard Brexiters have warned Theresa May that the only proposal they are likely to support to break the Brexit impasse is a version of the “Malthouse compromise”, which envisages removing the backstop from the draft European Union exit treaty.

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Steve Baker, the vice-chair of the European Research Group, said he and other Conservative Eurosceptics could not support the alternative they believed the prime minister favoured – an addendum to the existing EU withdrawal agreement.

Baker is one of five backbench MPs who will meet Steve Barclay, the Brexit secretary, on Monday, in the first meeting of a new working group aimed at examining whether technological solutions could eliminate the backstop.

The “Malthouse compromise” – named after the junior minister Kit Malthouse who brokered it – is a proposal to replace the unpopular backstop with alternative technological arrangements to prevent the return of a hard border in Ireland. It is supported by Baker, other Eurosceptics and the pro-remain former ministers Nicky Morgan and Damian Green, both of whom will attend further meetings with Barclay on Tuesday and Wednesday.

“As far as I’m concerned, the Malthouse compromise is the only game in town if we’re going to reach an agreement in Brussels,” Baker said, indicating that only rewriting the draft withdrawal agreement to remove the backstop would satisfy Tory Brexiters.

Last week, MPs voted in favour of an amendment in the name of Sir Graham Brady, a senior Conservative, to examine the possibility of new customs arrangements but it is unclear whether the necessary technology exists.

May also instructed Geoffrey Cox, the attorney general, to examine two other proposals that could be taken to Brussels: whether it would be possible to time-limit the backstop or to introduce a unilateral exit mechanism for the UK.

She is preparing to go to Brussels armed with specific proposals as to how to break the Brexit deadlock after the first deal May negotiated was defeated by 230 votes in January, the worst defeat suffered by a government in modern times.

But Downing Street insiders would not say when she hoped to travel, or even if it would be this week, and the prime minister is expected to spend Monday at No 10 working on her latest Brexit pitch to a sceptical and not obviously sympathetic EU.

Downing Street said it wanted to reopen the withdrawal agreement text regardless, but there was concern among Tory hard Brexiters that this was not the case. They said they believed that Cox was instead drawing up a “joint interpretative instrument” – a legal addendum refining aspects of the withdrawal agreement – which in effect would leave in place the backstop that has been denounced by the Tory right and the DUP.

Baker tweeted on Sunday morning that there would be “trouble ahead” if May was prepared to go along with what he described as a codicil – a message that he and the other two Brexiters, Marcus Fysh and Owen Paterson, on the new subgroup, were expected to reinforce when they meet Barclay on Monday.

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The justice secretary, David Gauke, who has threatened to resign if May pursues no deal, appeared lukewarm on Monday when asked about the likely success of the working group.

“I welcome an approach from parliamentary colleagues trying to be constructive, trying to find solutions,” he told BBC Radio 4’s Today programme, adding: “Let’s have a look at what those options are.”

Gauke also hinted a delay to departure seemed possible. Asked about this, he said: “We need to leave the European Union in a smooth and orderly way. Our objective is to do that on 29 March. But I think it is important it is a smooth and orderly departure, and that is key.”

On Sunday, the home secretary, Sajid Javid, appeared to back the idea of alternative technologies in a BBC interview, where he said that the Border Force government agency (which is in the Home Office) had shown him there was no need for a hard border and that the only thing missing was “goodwill on the EU side”.

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The cabinet minister also dismissed weekend newspaper reports that Downing Street strategists were considering holding a snap general election on 6 June if May could not get a Brexit deal through parliament.

“The last thing we want is a general election, the people will never forgive us for it,” Javid told The Andrew Marr Show on the BBC. “They want politicians to get on with the job. They have been given a very clear mandate, now it’s our job to get on with it.”

There are signs that the Conservatives have started to gear up for a possible snap election, with the party’s chief executive, Sir Mick Davis, having placed the Tories on a “war footing” last week and increased fundraising activities under the cover of the local elections in May.

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BuzzFeed reported that suggestions of a snap election had not gone down well with Tory MPs. According to leaked WhatsApp messages, it said the backbencher Conor Burns warned the party chairman, Brandon Lewis, that the election talk was “very unsettling” and demanded he rule it out. When he responded that the party HQ was focused on the local elections, it was dismissed as a “non-denial” and other MPs joined in, calling on him to rule it out completely.

A poll by Opinium for the Observer showed the Conservatives seven points ahead of Labour on 41%, but few people believe the party would risk going to the country under May’s leadership after the disaster of 2017, when the Tories lost their overall majority.

Javid said he believed there was no mileage in May trying to compromise with Labour and its leader, Jeremy Corbyn, on a deal that would keep the UK in a customs union with the EU after Brexit. He said he did not think such a deal would get a majority in the Commons, partly because “the other half of Labour say they want a second referendum” but also because “you would lose votes on the Conservative side, it’s a complete non-starter”.