A No 10 source has said a Brexit deal is “essentially impossible” after a call between the PM and Angela Merkel.
Boris Johnson and the German chancellor spoke earlier about the proposals he had put forward to the EU – but the source said she made clear a deal based on them was “overwhelmingly unlikely”.
Mrs Merkel’s office said it would not comment on “private” conversations.
But the BBC’s Adam Fleming said there was “scepticism” within the EU that Mrs Merkel would have used such language.
And the EU’s top official warned the UK against a “stupid blame game”.
President of the European Council Donald Tusk sent a public tweet to Mr Johnson, telling him “the future of Europe and the UK” was at stake.
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With efforts to get a deal by the end of the month on an apparent knife edge, Mr Johnson and his Irish counterpart Leo Varadkar have said they hope to meet later in the week.
But Mr Varadkar told an interviewer on Tuesday evening he thought it would be “very difficult” to secure an agreement by next week.
He said the UK had “repudiated” the deal negotiated previously with Theresa May’s government and had “sort of put half of that now back on the table, and are saying that’s a concession. And of course it isn’t, really”.
And following talks in Downing Street, the president of the European Parliament said there had been “no progress” and MEPs would not agree to a compromise deal “at any price”.
David Sassoli said the UK’s new proposed customs arrangements for Northern Ireland were a “long way from something to which the Parliament could agree”.