Theresa May is facing the threat of a Brexit backlash after an apparent breakthrough in talks in Brussels which could see the UK paying a “divorce bill” of as much as £50 billion.

Officials close to the negotiations were reported as saying there was broad agreement on a framework for the UK to settle liabilities expected to total around 45-55 billion euros (£40-£49bn).

If confirmed, the move could clear the way for the Prime Minister to finally achieve her goal of moving Brexit negotiations on to the issue of trade – though differences with Dublin over the status of the border in Ireland could still block progress at the European Council summit on December 14-15.

The reported deal was denounced by former Ukip leader Nigel Farage as a “sellout”.

“I have always argued that no deal is better than a bad deal,” he said. “Make no mistake about it – 55 billion euros to leave the EU is a very, very bad deal.”

A recent poll suggested that as few as 11% of voters would regard a “divorce bill” of £30 billion or more as acceptable. And former Cabinet minister Priti Patel said on Monday that the EU should have been told to “sod off with their excessive financial demands”.

But it is unlikely that either the EU or UK will ever put a final figure on the settlement, which covers a complex array of liabilities including funding for projects to which Britain signed up as an EU member, loans which have not yet been repaid, and pensions for European Commission civil servants.

Unofficial calculations have put the gross figure at around 100 billion euros, but deductions for items such as the UK rebate and Britain’s share of the European Investment Bank could reduce the net sum to about half that.

Payments would be made over many years as liabilities fall due, so the final total may not be known for decades.

Asked about reports of agreement on the financial settlement, a British Government source told the Press Association: “I don’t recognise it at all. There are ongoing discussions in Brussels this week.”

A spokesman for the EU’s chief Brexit negotiator Michel Barnier said: “We would not have any comment on it.”

But the BBC reported that officials on both sides of the talks were now discussing whether a paper can be prepared by next Monday, setting out formally what has been agreed so far, as a way of “parking” the divorce issues to allow negotiations to begin on trade and the transition to the future relationship.

Mrs May is due to meet European Commission president Jean-Claude Juncker on Monday for make-or-break talks which could determine whether Mr Barnier is able to declare that sufficient progress has been made to move the talks on to their second phase.

Theresa May with European Commission president Jean-Claude JunckerTheresa May will meet European Commission president Jean-Claude Juncker on Monday (John Stillwell/PA)

A recommendation from the French diplomat would spark intensive discussions in EU capitals over the 10 days before the European Council summit, at which any of the 27 remaining member states could wield a veto.

Downing Street declined to comment on an ITV report that the Cabinet agreed on Tuesday to a three-point package to secure a divorce deal. Two of the reported points – a pledge to keep the Irish border open and approval for a financial settlement topping £40 billion – were little different from what had previously been revealed.

But a supposed proposal to resolve concerns over the future rights of EU citizens living in the UK, by permitting the Supreme Court to refer issues up to the European Court of Justice where it felt unqualified to adjudicate, would be likely to prove more contentious. One senior Whitehall source dismissed as “nonsense” reports that this had been agreed by Cabinet.