OF THE various things Britain’s government has got wrong in its Brexit negotiating strategy, perhaps the most enduring is the belief that it could drive a wedge into the ranks of the remaining 27 members of the European Union.

A favourite early mantra of Brexiteer MPs was that German carmakers would pressure Angela Merkel to overrule other states (France, say) and let Britain cherry-pick the details of its new relationship. Then it was said that talks on the future relationship would provide an opportunity to exploit different interests among the 27. Over the summer ministers fanned out around the continent to woo potential allies. It was suggested that at the informal summit of EU leaders in Salzburg, which took place on September 19th and 20th, such states (the Netherlands, say, or Hungary) would insist on revising the terms of the European Commission’s negotiating mandate, giving Theresa May’s “Chequers deal” a chance of survival.

These hopes were dashed on September 20th when Donald Tusk, the president of the European Council, announced that the British proposal (which would effectively entail the country staying in the single market for goods but not for services) “will not work, because it risks undermining the single market”. In other words, the continental insistence on the integrity of the “four freedoms” of goods, capital, services and labour—voiced by Mr Tusk, Mrs Merkel and others throughout the process—is not fading. It was the bluntness of the president’s tone that prompted the most surprise among the British, who had expected emollience ahead of the summit in October, when the outlines of a deal are due to be thrashed out. Mrs May’s uncompromising tone at the summit dinner on the 19th seems to have contributed to the shift.

The death of the Chequers deal (never, perhaps, very alive) probably pushes Britain towards a looser, Canada-style, free-trade agreement as the basis for its future relationship with the EU. Yet with this arrangement it is harder to avoid a “hard border” between Northern Ireland and Ireland. And that is a red line for the EU, whose continued united support for the Irish government’s insistence on avoiding such a frontier has also defied some British expectations. Mrs May has just a month to devise a new, mutually acceptable solution. The chances of a chaotic, “no deal” Brexit have risen.

Yet if the summit was an education in EU unity on Brexit, the story was very different on the main subjects under discussion: security and migration. The block agreed on continuing operations against people-smuggling in the Mediterranean. It also approved a proposal by Sebastian Kurz, Austria’s chancellor, to launch formal talks with Egypt to reduce migration from the north African coastline (based on existing deals with Turkey and Libya).

Elsewhere, however, there was discord. Sweden wants mandatory quotas for migrant admission, in order to share responsibility around the union; Mrs Merkel has proposed that those not accepting migrants could make a financial contribution to states that do. Both ideas have been rejected outright by central European leaders like Hungary’s Viktor Orbán. There is no common ground on the overall number of asylum-seekers that the EU should accept.

Even a proposal that should be relatively uncontentious—the European Commission’s plan to increase the staff of Frontex, the EU border agency, to 10,000—elicited differences of opinion. Juha Sipilä, Finland’s prime minister, expressed reservations about how this force should be used. These doubts are shared by Mediterranean states, which fear that this centralisation would reduce the sovereignty of their own border forces. Mr Orbán is firmly against the measure, too.

In an illustration of the frustrations building over migration and borders, Emmanuel Macron made an extraordinary dig in his post-summit press conference. “Countries that don’t want more Frontex or solidarity will leave Schengen,” he said. “Countries that don’t want more Europe will no longer touch structural funds.” In essence he was suggesting that the likes of Hungary should be kicked out of the common travel area if they refuse to contribute to the EU’s reception of asylum-seekers and collaborate in common border policies.

It is no wonder, then, that EU officials are so keen to point to the common front established on Brexit. “Immediately after the [2016] referendum, we really worried about whether the 27 would hold together,” says one, marvelling that despite differing relations with the departing member, the remaining states have agreed that the integrity of the single market and the avoidance of a hard border on the island of Ireland deserve priority. At a time when, as Salzburg illustrated, so many other rifts are opening between the 27, Brexit, at least, remains a rare patch of harmony.