The German chancellor stood solidly behind the EU’s criticisms of the blueprint, which would see the reintroduction of customs checks on goods moving between Northern Ireland and the Republic of Ireland.
A Downing Street source said the German chancellor made clear in the telephone conversation – described as a “clarifying moment” – that a deal was “overwhelmingly unlikely” unless Northern Ireland was kept in the EU customs territory.
Mr Johnson is also said to have warned that talks were close to collapse because of the lack of movement, for which he blamed the EU.
The German Chancellery confirmed that Mr Johnson and Ms Merkel spoke on Tuesday morning but declined to confirm the substance of discussions, stating: “As usual we do not give an account of these confidential conversations.”
David Frost, the UK’s chief Brexit negotiator, returned to Brussels on Tuesday for more discussions – but there is little sign of any progress being made.
Asked if the talks were close to collapse, a No 10 source told The Independent: “That is what the prime minister told Merkel. They aren’t negotiating or engaging in Brussels.”
UK sources in Brussels however indicated that the meetings between the two teams were going ahead as planned.
A European Commission spokesperson said of the claim: "Technical talks are continuing today so I don't see how talks could have actually been broken down if they are happening today."
Asked about the comments attributed to Angela Merkel by Downing Street, the spokesperson told reporters in Brussels: "You're referring to comments that I have not seen the Chancellor herself has actually confirmed, so it would be first and foremost for the Chancellor and her team to provide a read-out from their side from what is reported with regards to a phone call earlier this morning.
"From out side what I can reiterate is that the EU position has not changed, we want a deal, we are working for a deal with the United Kingdom, and that under no circumstances will we accept that the EU wants to do harm to the Good Friday Agreement. The purpose of our work is to protect it in all its dimensions and at all times."
The tetchy early-morning conversation with the German leader is the latest in a string of setbacks for Mr Johnson’s latest round of capitals diplomacy – which has yet again been met with a united front from the EU side.
The prime minister had been told by Emmanuel Macron that the UK needed to redraw its plans by the end of the week, while the Dutch foreign minister warned on Monday that that more “realism and clarity” was required from the British.
EU leaders will meet in Brussels on Thursday and Friday next week, where Brexit will be discussed: both sides say they want a deal before the meeting. The European Council summit will also decide whether to extend Article 50, which would prevent the UK from crashing out on 31 October without a deal.
Mr Johnson has publicly said he will not seek an extension to the Brexit deadline, though court documents suggest he has privately promised to do so to comply with a law laid down by parliament. The UK is set to leave the EU with or without a deal at the end of October if no extension is secured, or the UK does not revoke Article 50 to cancel Brexit.
Under the British plan, Northern Ireland would stay aligned with the EU single market regulations for goods, but stay in the UK customs zone.
The result would be customs checks on products moving between the Republic of Ireland and Northern Ireland, and regulatory checks on products moving between Great Britain and Northern Ireland.
The UK government says the checks could be done away from the border, though has provided little detail on how – with critics warning the sites would be customs centres in all but name.
The Northern Ireland assembly and executive would also have to vote to keep the plan going every four years, effectively constituting a veto.
Critics of the UK government proposals, including most business groups and parties in Northern Ireland itself, are concerned that the reintroduction of a hard border would make infrastructure a target for dissident Republicans and disrupt the all-Ireland economy.
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