LONDON — Britain has made a Brexit bill offer — but with strings attached.

In a bid to unblock the Brexit negotiations ahead of the European Council in Brussels next month, the U.K. has dramatically expanded the scope of what it is formally willing to pay in ongoing financial commitments, a senior government minister familiar with the negotiations confirmed Wednesday.

After winning political agreement at home, Theresa May gave her chief Brexit negotiator Olly Robbins the green light to present a new, expanded formula to his Brussels counterparts for calculating the U.K.’s ongoing liabilities after it has left the bloc in March 2019.

While the final bill remains “guesswork” according to the government minister, it has been estimated to fall anywhere between £45-55 billion, sparking condemnation among some euroskeptics at home. Nigel Farage, the former UKIP leader, labelled it a “government sellout to the EU” which would “unite the British people in disgust.”

Since the start of negotiations, the EU has said the U.K.’s financial obligations include the so-called "reste à liquider" -- remaining sums to pay from commitments, some of them long-term, that the U.K. made as a member. The exact sum covered is unknown but has been estimated at around £30 billion by the U.K.’s former EU ambassador Ivan Rogers.

“This week is about agreeing the scope of our obligations — enough for sufficient progress anyway" — a senior U.K. official

However, the U.K. is still insisting that the offer is conditional on a final deal on future trading relations being agreed, the government minister said. It means that should the next round of negotiations break down in acrimony, any “deal” on money agreed this week could still be torn up.

Despite reports that a deal had been agreed between the two sides, a senior U.K. official involved in the talks insisted that both parties remained locked in negotiations to finalize an agreement that would clear the EU’s requirement for “sufficient progress” before the divorce talks can move to the next stage.

The next few days before the U.K. prime minister arrives in Brussels for lunch with Commission President Jean-Claude Juncker are crucial, the official said.

“It’s not so much a figure as a formula," the official said, "This week is about agreeing the scope of our obligations — enough for sufficient progress anyway.”

Both sides are now exploring the option of a joint letter that could be presented to the European Council as proof that sufficient progress had been reached to give them the political cover to allow the negotiations to move on to phase two — on the U.K.'s future relationship with the EU.

“This week is very delicate,” the official said. “A joint letter would represent an agreement on progress made on all fronts and be the convincer [EU negotiator Michel] Barnier can take to the 27 to say he’s happy it’s sufficient progress.”

May could well face domestic difficulties as well. One pro-European Labour MP said he worried the bill was so high it might not get through the Commons.

However, some prominent euroskeptics appeared willing to swallow the medicine. “We’re hoping very much that the offer the prime minister is able to make at that council will be one that guarantees sufficient progress,” Johnson told reporters on the sidelines of an EU-African Union summit, according to Reuters. “Now’s the time to get the ship off the rocks.”

The Conservative MEP Daniel Hannan said: “'Divorce bill' is the wrong phrase. What’s being argued over is how quickly we taper away our existing payments.”

Diplomats and officials in Brussels have moved to play down talk of an agreement being reached. However, there is widespread consensus that Britain has moved a long way since the Prime Minister’s Florence speech, when she indicated only a commitment to continue paying the current budget round finishing in 2020 and amounting to around £20 billion.

A senior EU Brexit official said: “No agreement has been presented to member states. Agreement has to be on paper, not in papers. We let the negotiators do their work and can’t comment [on] rumors.”

May’s political gamble to secure sufficient progress has caught some European capitals by surprise

A senior diplomat from one of the founding EU countries said “it’s something fed to the press that has not been translated yet into a negotiating position.”

May’s political gamble to secure sufficient progress has caught some European capitals by surprise.

One official close to the German government said they were surprised at how specific May was getting. From Berlin’s perspective, May would be wiser trying harder to mask the true cost in order to avoid a backlash.

Labour MP Chuka Umunna said that Brexiteers including the Foreign Secretary Boris Johnson and Environment Secretary Michael Gove had not been straight with the electorate.

“This is a whopping great symbol for the impossibility of delivering Brexit on the terms that it was sold to the British people,” he told the BBC's Today program. “People were not told we’d have to pay this.”

Jacopo Barigazzi and David Herszenhorn in Brussels, Charlie Cooper in London and Matthew Karnitschnig in Berlin contributed reporting.