French President Emmanuel Macron suggested that the bill could top 40 billion euro (£36 billion), saying that earlier indications that the UK could offer around 20 billion euro to ensure its EU partners were not left out of pocket due to Brexit did not go halfway to what was required.

The Prime Minister repeatedly dodged questions at the European Council summit in Brussels over how much the UK is ready to pay, insisting the size of a "full and final settlement" will not emerge until agreement is reached on all aspects of Brexit.

But she did not deny suggestions that it could be "many more billions" than the 20 billion euro indicated in her speech in Florence last month.

In a sign of the likely internal Tory battles ahead over the money, senior Brexiteer Bernard Jenkin warned Mrs May she should not sign up to a deal at any price, while pro-EU colleague Anna Soubry said it would be better to halt Britain's exit entirely than leave with no agreement.

Ms Soubry told BBC Radio 4's Any Questions: "I think people are coming round to this view, that actually no Brexit would be better than no deal".

Mr Jenkin said it was "reasonable" for the UK to help the EU out as it leaves but warned "if this becomes much more expensive than envisaged it is simply not worth it."

"The cost of paying tariffs on our exports to the EU would be less than half our annual net contribution.

"It is cheaper to pay for access to the single market by paying the tariffs than for us to be continuing to pay our subscription as a member of the EU," he told BBC News.

Mrs May said UK officials will spend the coming weeks going through Britain's financial commitments to the EU "line by line", ahead of a pre-Christmas summit when it is hoped leaders of the 27 remaining EU states will finally give the green light to the second phase of Brexit talks.

The EU27 took just 90 seconds to approve a programme of internal work on their position on trade in preparation for possible talks.

But they made clear that this step will depend on further progress being made on divorce issues including expats' rights, the Irish border and, in particular, the financial settlement.

In their formal conclusions, the EU27 said they aimed to move to the second phase "as soon as possible" and would reassess the state of progress at the next summit on December 14-15.

But they noted that Britain has so far made no "firm and concrete commitment" to settle all of its obligations.

Mr Macron said: "Much work needs to be done".

"I would say we are far from having reached the necessary financial commitments before we can open phase two," he said.

"We are not halfway there."

German chancellor Angela Merkel said a breakthrough in December "depends to a large extent" on the UK, adding: "The topic of financial commitments is the dominating issue in that regard."

Asked whether she would deliver further details on the divorce bill in time in order to secure progress in two months' time, Mrs May said: "What we are doing as we look across the weeks coming up to the December Council is looking at a range of issues ... On the financial issue, we will be going line by line through those commitments."

She indicated Britain will be ready to pay "relevant costs" of continued participation in EU projects in areas like science, research and criminal justice, but made clear that an overall figure cannot be expected before the shape of the final deal is known, something that is not expected before autumn 2018.

As expected, the EU27 backed chief Brexit negotiator Michel Barnier's assessment that insufficient progress has been made in divorce talks for trade discussions to start now, as Britain had hoped.

But the agreement to begin scoping work on trade may reassure City firms which had suggested they might have to move functions and staff to the continent if no progress was made by Christmas.

Mr Macron said the Prime Minister did not mention the possibility of a no-deal outcome when she addressed EU leaders over dinner on Thursday evening.

He suggested the idea could be "bluffing" by "secondary players".

European Council president Donald Tusk said "reports of the deadlock between the EU and the UK have been exaggerated" and that he wanted to be a "positive motivator" to clearing up remaining issues over the next five or six weeks.