Theresa May, shortly after seeing off the rebels seeking to dethrone her, took to the steps of Downing Street to tell of her intention to secure “legal and political assurances” on the backstop in the withdrawal agreement to “assuage the concerns that members of parliament have on that issue”.

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By threatening to keep the UK in a customs union, the Northern Ireland backstop for avoiding a hard border in effect torpedoes Brexiters’ dream of a “global Britain” able to strike trade deals around the world, and set its own regulatory path, free from Europe. With Northern Ireland also due to stay in the single market, the Democratic Unionist party says it amounts to breaking up the United Kingdom.

Of the 117 Tory MPs who voted against the prime minister, there will be a fair few who will only be sated by the backstop being ripped out from the withdrawal agreement, the line taken by the DUP. There is no hope of this coming to pass, and the prime minister knows it.

Others, including many MPs who did not vote in favour of ousting May, grudgingly accept that the backstop must remain, but have one central demand: they want a ready exit mechanism, or time-limit, to convince them that the UK will not be trapped in it.

The first step in the EU’s response has been to offer some moderately warm, but ultimately weak, words of reassurance. At the summit on Thursday evening, the leaders reiterated that they would seek to find an alternative arrangement before the end of the transition period to avoid it being implemented. In any case it would be temporary should it come into force, and Brussels “would use its best endeavours to negotiate and conclude expeditiously a subsequent agreement that would replace the backstop, and would expect the same of the United Kingdom”.

A paragraph was deleted from an earlier draft that had offered a tantalising glimpse of their potential second step, and of the debate that is now still raging among the EU27 member states. “The union stands ready to examine whether any further assurance can be provided,” the leaders were going to say. “Such assurance will not change or contradict the withdrawal agreement.” It is surely still the plan.

May is seeking to attach a “joint interpretative instrument” to the withdrawal agreement, which would extrapolate from the commitments to make “best endeavours” to get out of the backstop that already exist. Such a device was used in 2016 to reassure the Belgian region of Wallonia when it was holding back on the ratification of the EU-Canada trade agreement.

The British government wants to put a duty on both sides to make all efforts to get out of the backstop within one year of it coming into force. But it is proving a very hard sell.

While the Austrian chancellor, Sebastian Kurz, expressed his hopes of offering such “legal and political assurances” at the summit on Thursday, and Germany is in favour, others including the Dutch prime minister, Mark Rutte, and the Finnish prime minister, Juha Sipilä, spoke of difficulties in even considering a legal interpretation to go with the treaty. Spain is highly sceptical. And Belgium has privately warned that the Brexiters will just come back for more, describing it as “a carousel”.

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The French president, Emmanuel Macron, who has emerged as the pantomime villain in these Brexit talks is said to be firmly opposed. Meanwhile, the Irish prime minister, Leo Varadkar, admitted that during his “long meeting” with May in the margins of the summit, there had not been a complete meeting of minds. “Some of the suggestions she made, made sense, others I thought were difficult”.

The EU and the British government agree that they will not reopen the withdrawal agreement, for fear of the whole thing unravelling. By providing legal interpretations, Macron and others fear that they are tinkering with the backstop via the backdoor.

But more significantly, the prime minister’s brush with the political dustbin on Wednesday night has also upped the level of scepticism about such legal tinkering making an impact on May’s chances of getting her deal through parliament. “Some sceptics are not really using rational arguments”, the baffled Austrian chancellor remarked. The EU’s leaders want to help – but would it really make any difference?