Following a working lunch of the remaining 27 European Union states at the informal summit in Salzburg, Mr Tusk said that while there were "positive elements" in the Chequers plan, they could not accept any proposal which threatened the single market.

Speaking at an informal European Union summit in Salzburg, Austria, Maltese Prime Minister Joseph Muscat told the Today programme: "I think most of us would welcome a situation where there is the possibility of the British people putting things into perspective, seeing what has been negotiated, seeing the options and then deciding once and for all".

But with time running out for the United Kingdom to reach a deal, Ms Davidson said: "It is absolutely right that people have their say about what sort of Brexit they want, but we are right down to crunch time now, we're talking weeks not months".

"The Brexit teaches us something - and I completely respect British sovereignty when I say that - it showed that those who say that we can easily live without Europe, that everything is going to be alright, and that it's going to bring in a lot of money are liars", he said.

That would lead to Britain crashing out of the European Union on Brexit day, a development that in theory could see flights parked and trade between the two sides grind to a halt. "A minister has had the courage to tell the truth about the mess the government are in over Brexit and let the cat out of the bag", she said.

Labour MP Jo Swinson, from the People's Vote movement pushing for a second referendum on Brexit, said "Chequers is dead" and "whatever comes out of the negotiations now will inevitably be a very bad deal for Britain".

For now, however, with May still facing criticism of her "soft Brexit" approach at her Conservative Party conference in 10 days, there was little sign of either side giving way.

Sterling slid around more than half a cent against the dollar after the report to a low of $1.3098 before edging slightly higher to last trade at $1.313.

In a letter to opposition leaders at Westminster, Nicola Sturgeon yesterday called for the Brexit timetable to be extended in the event that no deal is reached, to "avoid an economic cliff edge".

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Mrs May's 27 European counterparts will now consider the next stage of the Brexit process after she told them her Chequers plan was the only credible route to a deal.

"We need to compromise on both sides", Tusk noted.

"It must be clear that there are some issues where we are not ready to compromise".

"It was clear today that we need substantial progress by October and that we then aim to finalize everything in November", said German Chancellor Angela Merkel.

Over dinner, she said the problem could be solved by securing the type of "frictionless trade" envisaged in her Chequers plan, and that Britain was still committed to agreeing a fall-back scheme with the EU.

"Unfortunately we can not at this stage exclude a no-deal - it depends on both sides of negotiations".

Speaking in Salzburg, Mrs May insisted that "delaying or extending these negotiations is not an option", no matter how much leaders disliked her plan.

But pro-Brexit firebrand Nigel Farage responded on Twitter saying: "EU bosses want us to have a second referendum, quelle surprise".

May held one-on-one talks on Thursday with Irish Prime Minister Leo Varadkar, who had earlier told the BBC: "I don't think we're any closer to a withdrawal agreement than we were in March".