Earlier, Michel Barnier, the EU’s chief negotiator – who was described as “very downbeat, very gloomy” by the Irish government – told MEPs the negotiations would not carry on beyond Wednesday.
As hopes of a deal were fading fast, Mr Johnson and Ms von der Leyen emerged from a 90-minute phone conversation to announce they would meet, raising fresh expectations of a last-gasp rescue.
“We agreed that the conditions for finalising an agreement are not there due to the remaining significant differences on three critical issues: level playing field, governance and fisheries,” their statement said.
“We asked our chief negotiators and their teams to prepare an overview of the remaining differences to be discussed in a physical meeting in Brussels in the coming days.”
Offering one significant olive branch, the prime minister did back down by agreeing to drop the clauses in the Internal Market Bill that would break international law, if a deal could be struck.
Despite this offer, all but 15 Conservative MPs voted just hours later in the Commons to reinsert the offending clauses, following their removal by outraged and concerned peers.
With just 24 days to go to the UK crashing out of the single market and customs union, both sides agree they remain far apart on the crunch disputes of access to UK fishing
The UK admitted the so-called “level playing field” issues – to stop any weakening of labour or environmental standards, or subsidy limits – were the biggest obstacle to an agreement.
And, late on Monday, the UK appeared to have made a deal on fishing even more remote, by reportedly proposing to strip them out of the talks altogether.
It leaves the UK staring at the abyss of a crash-out Brexit, on 31 December, that is forecast to strip £40bn off GDP – 2 per cent of the total – next year alone.
But, answering an urgent question in the Commons, Cabinet Office minister Penny Mordaunt faced repeated demands from Tory MPs to rule out any compromises by the UK side.
Laying bare the pressure on the prime minister not to give way, Iain Duncan Smith, the former Conservative leader, said what mattered most was “continued control of our laws, territorial waters and our trade”.
Ms Mordaunt acknowledged: “Familiar differences remain on the so-called level playing field, fisheries and governance”, adding: “Of these, the level playing field issue is currently the most difficult.”
And, on reclaiming fishing rights in UK waters, she told one worried Tory: “He has my assurance that the prime minister will not compromise.”
Crucially, Mr Barnier set the new deadline of Wednesday for the negotiations, as he told diplomats they were “not far from the very endgame”.
Simon Coveney, Ireland’s foreign minister, said: “The news is very downbeat. I would say he is very gloomy, and obviously very cautious about the ability to make progress today.”
In other developments:
– Northern Ireland businesses warned a no deal would place it under “unbearable and unnecessary strain at a time of crisis” – urging Mr Johnson to “redouble your efforts”.
– No 10 admitted that leaving the EU on “Australia terms” will mean no deal and trading on World Trade Organisation terms, with its tariffs and quotas.
– European trade unions warned Mr Barnier of their fears that any compromises would allow the UK to undercut workers’ rights in the bloc.
Downplaying expectations ahead of Mr Johnson’s trip, one government source stressed: “Talks are in the same position now as they were on Friday. We have made no tangible progress.
“It’s clear this must now continue politically. Whilst we do not consider this process to be closed, things are looking very tricky and there’s every chance we are not going to get there.”