Theresa May has told the European commission president, Jean-Claude Juncker, she needed “legally binding changes” to the Irish backstop if MPs were to back her Brexit deal, during a high-stakes meeting in Brussels that yielded no obvious breakthrough.

With only 37 days until the UK leaves the European Union, EU expectations were low when May arrived in Brussels. Shortly before meeting the prime minister, Juncker predicted there would be no breakthrough.

A joint statement on Wednesday appeared to live up to that promise, but the two leaders promised to talk again before the end of the month and described talks as “constructive”. The two sides said they were “seized of the tight timescale and the historic significance of setting the EU and the UK on a path to a deep and unique future partnership”.

In an olive branch to May, the EU’s chief Brexit negotiator, Michel Barnier, and the Brexit secretary, Stephen Barclay, were tasked with looking at the role “alternative arrangements” could play in replacing the contested Irish backstop in future.

But the EU continues to rule out changes to the backstop, which is intended to prevent a hard border returning to the island of Ireland.

Speaking after the meeting, May said she had “underlined the need for us to see legally binding changes to the backstop which ensure it cannot be indefinite. That’s what is required if a deal is going to pass the House of Commons.

“Time is of the essence and it’s in both our interests that when the UK leaves the EU it does so in an orderly way,” she said.

Before the encounter, Juncker met Slovenia’s president, Borut Pahor, who voiced hope a deal could be reached while stressing he backed Ireland over the backstop: “Something not acceptable to Dublin would not be acceptable to Slovenia either.”

At the same press conference Juncker joked that May was not to blame for a shaving injury to his cheek. “You will have noted that I have the outcome of an unfortunate gesture this morning,” he said referring to a plaster on his face. “I am just telling you this because I don’t want you to think that Mrs May is responsible for this injury.”

Privately, officials are in no joking mood, with frustration over Brexit “groundhog day” running high. One senior EU diplomat said May was to blame for failing to confront hardline Eurosceptic Tories. “She gave the impression that you can stay in your delusional comfort zone, but you can’t,” the diplomat said. “Unless she is ready to choose there is nothing we can do.”

The government has backed away from hopes of rewriting the Brexit withdrawal treaty. May hopes for stronger guarantees that the backstop would never come into force. Barclay and the attorney general, Geoffrey Cox, are due in Brussels on Thursday for further talks. Cox is seen as a pivotal figure in Brussels, as officials think any change in his legal advice could persuade Tory MPs to back the deal.

According to senior figures in the UK government, Cox’s plan A is a “codicil” that would allow the UK to quit the backstop unilaterally with one year’s notice. While some cabinet ministers think it is promising, it is likely to get short shrift in Brussels. The EU has long ruled out any unilateral exit mechanism, insisting that any additional legal text cannot contradict the existing Brexit deal.

The two sides are working on a legal document that would firm up existing guarantees that the backstop would never be used. Sterling rose after Spain’s foreign minister, Josep Borrell, said progress was being made on a text. “The EU’s position is that the treaty won’t be reopened, but can be interpreted, or complemented with explanations that may be satisfactory,” he told Bloomberg.

EU diplomats in Brussels sounded a more sceptical note. Many doubt that that a legal text that does not alter the backstop could win over Tory Eurosceptics. One said it “didn’t seem realistic” such a text would change anything in the UK parliament. “This fudge language, which is part of the British political tradition, doesn’t really work with EU law,” the diplomat said.

The recent spate of defections from Labour and the Conservatives is seen as complicating the prime minister’s quest for a majority. “It makes it difficult for any British government to negotiate,” the diplomat said.



