ON SEPTEMBER 21st Theresa May did something that she almost never does and delivered a live broadcast to the nation from Downing Street, on the state of the Brexit negotiations. This is a measure of how stunned Mrs May was by the debacle at the meeting of European heads of government in Salzburg the previous day.

Before that meeting, things had been looking good for the prime minister. The Brexiteer-ultras had overplayed their hand. Boris Johnson, her would-be replacement, was looking like a busted flush. Mrs May’s key advisers briefed that Brussels might be willing to compromise on the remaining sticking-points of Britain’s withdrawal agreement. This week’s Bagehot column made the mistake of buying into this optimistic argument.

Salzburg delivered a slap in the face to Mrs May (and forced Bagehot to eat his hat). The European establishment not only said that her proposed Brexit deal, hammered out in July with her cabinet at Chequers, her country retreat, was dead. It did so in the rudest way possible. EU leaders left Mrs May isolated. Emmanuel Macron delivered a self-satisfied lecture on how foolish the Brexiteers were (Vladimir Putin apparently nicknames the French president “Macron-and-on-and-on” because of his habit of delivering lectures). Donald Tusk, the president of the European Council, posted an Instagram picture of himself offering Mrs May a cake, with the line “Sorry, no cherries,” a reference to the “cherry-picking” of which Brussels has repeatedly accused Britain.

In her televised address, Mrs May admitted that Britain and the EU had reached an “impasse”. There are two big, interconnected issues where the two parties remain as far apart as ever, an astonishing situation after a year-and-a-half of negotiation. The first is their broad economic relationship after Britain leaves the EU. The EU rejects Mrs May’s Chequers compromise, which in effect would have involved Britain’s partial membership of the single market. Instead it has offered Britain two options. One is a Norway-style deal, which would force it to obey nearly all the bloc’s rules, including freedom of movement—something that would make a mockery of the referendum, Mrs May said. The other is a more limited, Canada-style deal, which would mean greater barriers to trade.

The second area of disagreement concerns the status of Northern Ireland. Both parties agreed in December that whatever happens, the border between the north and the Republic of Ireland must remain open and invisible. Britain argues that this could be achieved by carrying out customs checks away from the border; the EU rejects this and suggests the checks be carried out between Northern Ireland and Britain, in effect creating an economic border in the Irish Sea. Mrs May said that was unacceptable.

She repeated her position as firmly as possible: she is neither willing to betray the Brexit vote nor to break up the United Kingdom. She also added a sting in the tale about the EU’s tone: “I have treated the EU with nothing but respect. The UK expects the same.”

Despite her bulldog tone, there is no doubt that Mrs May is in a desperate situation. The EU has made it clear that it will not accept the Chequers compromise, which she sweated blood to produce. Mrs May’s critics on both the right and the left of her Conservative Party feel vindicated. Brexiteers regard Chequers as a hopeless fudge because it would force Britain to bind itself to most of the EU’s rules, without any say in making them. “Vassalage” is how both Jacob Rees-Mogg and Boris Johnson describe it. Many Remain-voting Tories, meanwhile, such as Justine Greening and Nick Boles, think that Britain would be better to adopt something like the Norway option rather than the over-complicated Chequers plan.

Mrs May prides herself on her stubbornness. But stubbornness can turn into pigheadedness if it is not tempered by realism. The big argument in favour of Chequers is that it is a pragmatic compromise—nobody’s first choice, but something that might bring London and Brussels, and Brexiteers and anti-Brexiteers, together. It is now looking increasingly unlikely that Chequers can provide even the basis for a compromise. Mrs May needs to beware pouring yet more time and energy into a doomed policy.

The Salzburg debacle has darkened the mood of British politics. Tories of all description are furious that their leader has been treated so shabbily by Eurocrats. The Tory party conference, which begins in Birmingham on September 30th, will be an unusually angry and bitter affair. Brexiteers feel vindicated in their view that it is impossible to deal with the European bureaucracy. And practical-minded people are getting increasingly worried that Britain will fall out of the EU without a deal. The pound fell in the aftermath of the Salzburg meeting.

There is plenty more drama to come. This autumn could see the British political system seize up as Mrs May fails to produce a majority for any Brexit deal, the government fails to prepare a fallback position, and Parliament engages in noisy squabbles about various alternatives. Such paralysis in turn could produce four possible outcomes: a general election, a second referendum, a disorderly exit from the EU and a delaying operation.

Mrs May’s dream of a clever fudge that would secure Britain’s orderly exit from the EU without damaging the economy or disrupting the mainland’s relationship with Northern Ireland increasingly appears the least likely option.

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