Theresa May is suffering a major backlash from all wings of her party after telling European Union leaders she is willing to extend the Brexit transition period by up to 12 months in an attempt to unlock negotiations.
German Chancellor Angela Merkel described finding a solution as "squaring the circle".
So uncertain was that prospect that a special European Union summit on Brexit that had been penciled in for next month to finalize a deal was taken off the table.
"Mrs May's Brexit betrayal slowly slithers into view", said Ukip leader Gerard Batten.
Earlier this month, the French government unveiled draft legislation aimed at setting out preparations for a possible no-deal Brexit which would cover British citizens living in France and French nationals in Britain. "The key element is a British political compromise".
But Lithuanian president Dalia Grybauskaite said there would be "no breakthrough" this week because May lacked a strong mandate from her party and parliament.
A longer transition would, for them, simply extend the period of "Brexit in name only".
Dutch Prime Minister Mark Rutte, traditionally an ally of May's in the bloc, said "we have the instruments on the table and it should be doable".
"More than ever, the ball is in Britain's court", said Belgian Prime Minister Charles Michel as he arrived for Thursday's talks.
On Thursday British Prime Minister Theresa May angered many of her Tory MPs, when she revealed one option that had emerged from talks in Brussels with the 27 European Union leaders, was an extension of the "implementation [or transition] period for a matter of months" - in an effort to break the deadlock over the Irish border issue.
European leaders had hoped to hold a special summit in November to seal the divorce, but at a Brussels dinner without May late Wednesday they refused to sign off on the plan.
An EU official, who spoke to Germany's dpa news agency on the condition of anonymity, also said May had said she was "ready to consider" an extension to the 21-month transition period after Brexit. But May's team is "considering the move", because it would be a "simple way to buy more time to agree a UK/EU trade deal, which is meant to remove the need for the Irish border backstop guarantee". It's a good idea.
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"We noted in particular the need to closely watch the situation in the Western Mediterranean, and in this context, to strengthen our cooperation with Morocco, as recommended by (Spanish) Prime Minister (Pedro) Sanchez", said Tusk in a press conference after the summit.
Jean-Claude Juncker, the head of the European Commission, which is the EU's executive branch, also welcomed the idea.
"We cannot find the money to fund our front-line police properly, we cannot find the £2 billion for the vulnerable on Universal Credit, but we can mysteriously find billions to bung to the European Union for the unnecessary extra year Clegg and Blair asked Barnier for to waylay Brexit", said Ms Dorries.
Furious Brexiteers said that the move would delay yet further the moment when the United Kingdom could sign new trade deals around the world, and would cost taxpayers billions of pounds in additional contributions to the EU.
Asked about the plan, a British official said there were no plans to propose a change to the transition.
British Prime Minister Theresa May is still hopeful of negotiating a withdrawal deal from the EU.
European Research Group chairman Jacob Rees-Mogg said it would mean "we are in the EU for longer when the EU can make rules for the United Kingdom over which we would have no say - and we would be paying for the privilege".
But UK Government officials said "momentum" was growing and outstanding disagreements could be resolved over the next few weeks.
Merkel said: "Where there's a will, there should be a way". "But it's maybe a more emotional impression than a rational one".
Speaking after Tusk and Juncker, May said Thursday that there would be more hard moments ahead as they reach the final stages of the talks, but added that she was confident in her ability to secure a good deal that is agreeable to all parties.
Britain has proposed staying temporarily aligned to the EU's customs rules, but the bloc wants this to have no end date - something her eurosceptic MPs will not accept.
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