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 put forward to the EU – but the source said she made clear a deal based on them was “overwhelmingly unlikely”.
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, writing: “What’s at stake is not winning some stupid blame game. At stake is the future of Europe and the UK as well as the security and interests of our people.”
Ireland’s Tánaiste (Deputy Prime Minister), Simon Coveney, tweeted it was “hard to disagree” with Mr Tusk, writing: “We remain open to finalise a fair Brexit deal, but need a UK government willing to work with the EU to get it done.”
Mrs Merkel’s spokesman said her office would not reveal details of “private, closed” conversations.
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The BBC’s Europe editor Katya Adler said it was “no secret” Berlin found the UK’s proposed new customs solution for Northern Ireland problematic, but it had not yet given up hope.