An English country house, a polite but inscrutable host and an ill-assorted band of guests, each with a motive to stab each other in the back. Theresa May’s Brexit house party at Chequers next Friday sounds more like the set-up for an Agatha Christie mystery than a cabinet meeting.

But drumming up a sense of drama has become another tool in the prime minister’s battle to unite her scrapping ministers. So, a full two years on from the referendum, she will gather them for a day-long summit and a working dinner next Friday.

So many crunch moments and make-or-break meetings have passed without the anticipated showdown since article 50 was triggered last March, that one Brexiter has taken to calling Downing Street “Old Mrs May’s fudge shoppe”.

However, ministers are being carefully prepared, with face-to-face meetings with David Davis – or May’s chief of staff, Gavin Barwell – increasing speculation that Chequers could be a more decisive meeting than most.

Government insiders say May’s direction of travel is becoming increasingly clear – and it’s towards a softer Brexit. The question swirling at Westminster is how much further she can push the leavers in her cabinet in that direction, and whether some could choose to walk out rather than sign up.

Her chief Brexit negotiator, Olly Robbins, is expected to guide the discussion, by setting out the broad options the UK faces – and the tradeoff.

With time growing increasingly short, insiders say he is likely to focus on off-the-shelf models – from an intimate, Norway-style relationship, with single market membership for goods, and signup to EU rules and regulations, to a far looser, free trade deal – what David Davis has called “Canada plus plus plus”.

Spooked by dire economic warnings about the risks of economic damage from Greg Clark’s business department and Philip Hammond’s Treasury (the “heart of remain”, as Boris Johnson was recorded calling it recently), the prime minister is widely believed to be moving towards the former.

But single-market membership – even just for goods – would ride roughshod over the government’s red line on European court of justice oversight, and leave the UK as a “rule-taker” in key areas.

It would also require the UK to make a very generous offer on migration.

Such a package would stray perilously close to what the leavers call “BRINO” – Brexit in Name Only – and some could find it hard to reconcile with the reasons they backed leave in the first place.

Theresa May at the EU summit, where she faced criticism from other leaders. Photograph: Isopix/Rex/Shutterstock

By assembling her full cabinet, rather than the finely balanced Brexit strategy and negotiations committee, on Friday, May will increase the chance that she can carry the room – though the stance of several of her most ambitious ministers is far from clear.

Sajid Javid and Gavin Williamson have both previously sided with the Brexiters over future customs arrangements, an issue that has still not yet been resolved. And Jeremy Hunt raised eyebrows last week by joining criticism of Airbus for intervening in the Brexit debate. All are regarded as potential future leadership candidates.

Brexiters are girding their loins for a fight. They feel they have already accepted a string of compromises, from the £40bn “divorce bill” to the transition period – and now potentially a “temporary customs arrangement” even after that, when the UK would continue applying the EU’s external tariff to imports.

“If they try to go down the Norway route, and push it hard, she’s got a real problem,” said one senior government source.

Sajid Javid has previously sided with the Brexiters. Photograph: Dinendra Haria/Rex/Shutterstock

In Brussels, where May faced criticism from a string of leaders on Thursday, which continued on Friday after she left, puzzlement about Britain’s indecision has turned to exasperation.

The shadow Brexit secretary, Keir Starmer, who held a series of meetings with senior figures in Brussels earlier this week, says: “They’re getting fed up with the idea that there are ‘party management issues’ that have to be dealt with.”

Negotiators long for a clear answer from May next week – and in the white paper she will publish a few days afterwards – about the future relationship.

Senior Brussels officials say that, with direction from London, they could be ready to work up a deal well before the October deadline. But they fear December looks increasingly likely.

They are anxious too that May could expend precious domestic capital on winning round truculent leavers to a solution that will still be simply unacceptable in Brussels.

The commission is adamant that a single market for goods alone is not on the table, even alongside customs union membership.

Aside from repeating Michel Barnier’s familiar refrain about the “indivisibility” of the single market, they point to the high service content in many goods (design, engineering and so on). They fear the UK would thus be able to undercut the EU27 by giving favourable tax or regulatory treatment to services.

As the UK itself used to acknowledge when pushing to deepen the single market, a “level playing field” is about much more than just tariffs.

Downing Street continues to hope there is an outcome that falls short of a Norway arrangement, but avoids some of the pitfalls of Canada. In Brussels, they say no chance.

The two sides also remain miles apart on how to avoid a hard border in Ireland. Barnier told reporters on Friday that “huge and serious divergence remains, in particular on Ireland and Northern Ireland”. The UK’s backstop proposal – hard-fought in cabinet – has been rejected outright.

Sidestepping a row is one of May’s greatest skills, and next week’s house party could yet be a convivial one. But so deep are the fissures in her cabinet – and so poisonous the mood – you don’t have to be Agatha Christie to imagine it could end with blood on the carpet.

