It was the moment that pro-Remain Conservative MPs had been longing for, but feared would never happen – when the prime minister cut the arch-Brexiter Jacob Rees-Mogg down to size. One MP who witnessed Theresa May’s newfound assertiveness likened it to a long-suffering teacher finally losing patience with the class know-all. “She just slapped him down, decisively. She showed she can do it. She was brilliant.”

Five groups of about 30 Tory MPs at a time had been asked into the chief whip’s office in No 9 Downing Street last Monday. May’s chief of staff, Gavin Barwell, had been told to brief them on the two options for solving the seemingly intractable Irish border problem that threatens the Brexit process.

After Barwell had done his bit, May made herself available for questions. By chance, Rees-Mogg’s batch of MPs included leading names from the parliamentary party’s voluble Europhile wing. Kenneth Clarke, Anna Soubry and Dominic Grieve were there representing Remainers.

When Rees-Mogg got his chance he was quick to ask the prime minister why she could not do what seemed the obvious thing for a hard Brexiter like him – forget any deal and just keep open the border after Brexit. “He was basically calling for a no-deal,” said another who attended.

May has often been accused of sitting on the fence on Brexit, of failing to give a lead and ducking out of confrontations with either side in her split party. On this occasion, however, she broke that habit and gave Rees-Mogg a piece of her mind. According to several sources, she spelled out in no uncertain terms the serious problems and costs that would result from having to resort to World Trade Organisation rules, while also stressing the potentially grave security dangers that would follow if and when the Republic of Ireland had to reimpose border controls on the orders of the EU in order to preserve the integrity of the single market.

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“It was the most amazing moment when the Rees-Mogg claptrap finally met cold reality,” said one Remain MP who attended. “She became animated in a way she doesn’t normally, she was completely engaged, not robotic at all. She was really concerned about the security issue and she showed she really meant every word she said.”

For several weeks May and her cabinet had failed to agree what to do about the customs issue – how to avoid a hard border in Ireland without remaining inside the EU customs union and possibly the single market too.

For a long time May had pushed a “customs partnership”, under which the UK would collect tariffs for the EU, post-Brexit – an idea vetoed by the Brexiters in cabinet, led by Michael Gove and Boris Johnson, on the grounds that the UK would in effect still be tied in with a key pillar of EU bureaucracy and the Brussels economic model. Instead, the Brexiters favoured relying on as yet unproven technological solutions to track cross-border trade. Neither Brussels nor most experts in the field believed either option was really workable.

No one could see a way forward. Then with the clock ticking towards a Brussels summit next month, at which the UK is expected to have its plan for the Irish border agreed, and with the Irish warning that unless the UK puts forward some solutions it could leave the EU without any deal, May shifted her approach, as the extent of as yet unresolved problems piled up around her.

A senior government source close to the Brexit talks said that had she not done so she could have been submerged: “It is not just the Irish problem that there is no agreement on. Almost everything needs to be sorted out and we are running out of time. You name it, we have not agreed it. We cannot be held up by these few hardliners for ever.”

The day after (Tuesday) there were further signs of May’s newfound pragmatism and willingness to face down the likes of Johnson and Gove inside the cabinet, and Rees-Mogg and the 20 or so Brexit ultras from the backbenches.

At a meeting of the cabinet Brexit subcommittee, a report from the Cabinet Office secretariat proposed a compromise on the Irish question that would, if need be, offer a so-called “backstop” option under which the UK could remain tied to an EU customs union for an unspecified period after the two-year post-Brexit transition deal ends in 2021. Under such a scheme, the whole of the UK would be covered by the EU external tariff during that as yet unlimited period, thereby removing any requirement for a border either between the republic and Northern Ireland or between Ireland and the UK.

“That is a big deal, a big move, a big acceptance of reality,” said one pro-Remain Tory MP last Thursday. “That is why the Brexiters hate it.”

The Brexiters knew that, assuming the plan is acceptable to Brussels (which it may well not be), it would mean them accepting that the UK would remain subject to customs union and single-market arrangements (in so far as either affects border issues) for more than two years after Brexit day on 29 March 2019. It was yet more slippage.

Facebook Twitter Pinterest Jacob Rees-Mogg ‘was basically calling for a no-deal’, according to those who attended the meetings with the PM. Photograph: Bloomberg

Government sources said most cabinet ministers at the meeting received little or no notice of the proposals, suggesting that May presented them as a fait accompli. Gove and Johnson, say insiders, suggested putting time limits on the number of months (or years) the backstop could apply for after March 2021. But no limit was agreed. No 10 did not want one. “There were plenty of time limits which were not agreed,” said an insider. “She called their bluff and it worked.”

The change of approach was clear, and significant – but in a sense it was all May could do if multiple Brexit crises were not to completely consume her government. As well as negotiating with Brussels, she still has to steer heavily amended and contentious Brexit legislation through parliament without a working majority behind her. Tory Remainers believe they have the numbers to defeat the government on several key votes in order to deliver the soft Brexit they want.

On all sides, though, there are now more signs of realism entering the debate. Tory Remainers are busy trying to find what they call “pragmatic Brexiters” with whom they can make common cause to avoid too much deadlock. The fear of Jeremy Corbyn’s Labour party exploiting Tory chaos has brought some Conservatives to their senses.

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Plenty of Tory Brexiters are also aware more time may be needed to ensure that their preferred option of breaking free from Brussels customs rules, known as “maximum facilitation” or “max fac”, is viable.

Nick Boles, the modernising Tory MP, proposed extending Britain’s membership of the customs union until just before the next election in 2022. Former Tory and Ukip MP Douglas Carswell said it was a “sensible” move. Boles is keen to push the idea and is prepared to submit it as an amendment to Brexit legislation.

Extending membership of the customs union could appeal to some Tory MPs in both the Remain and Leave camps, as it would in effect delay a number of key decisions about the longer-term relationship with the EU, and keep options open. At the same time, however, some Remainers are growing more confident that they can win a vote on a plan that keeps Britain close to a customs union for the long term.

As one former minister put it, Brexiters are having to confront some “basic realities” about life outside the EU – and the fact that you cannot get anywhere without trade-offs and patience. “The Olympics took seven years [to prepare for]. It was a two-week sporting event,” one said. “Unless there’s a plan and you can deliver it, then it’s likely [that we’ll stick to the] status quo until then. It’s not a compromise. It’s just a fact people have to accept. Similar to the fact that the Earth isn’t flat.”