Britain has bowed to EU demands and agreed to fully honour its financial commitments as identified by Brussels, removing one of the biggest obstacles to a Brexit divorce settlement.

According to several diplomats familiar with the talks, the UK would assume EU liabilities worth up to €100bn although net payments, discharged over many decades, could fall to less than half that amount.

Prime Minister Theresa May is expected to formally present the breakthrough offer next week as part of a package deal if agreement can be reached on the other issues of citizen rights and the contentious question of the border between Northern Ireland and the Republic.

The pound was 0.5 per cent higher at $1.3404 on Wednesday morning, taking its rally against the dollar since the news broke overnight to just over 1 per cent.

Against the euro, sterling was 0.2 per cent stronger, with £0.8856 required for a unit of the shared currency.

The overture on the bill was made by Olly Robbins, the British prime minister’s lead official on Brexit, in discussions with the commission last week.

Negotiators are working on how to present the settlement as a net estimate, with the UK side pressing for an implied figure of between €40bn and €45bn once UK receipts and other deductions are taken into account. “They have promised to cover it all, we don’t care what they say their estimate is,” said one senior EU diplomat. “We’re happy to help them present it.”

Intensive negotiations are continuing, with the aim of declaring “sufficient progress” next week on the financial settlement, citizen rights and Northern Ireland. Discussions are delicately poised and negotiators have warned that a hold-up on any one element of talks could scupper a December deal to open trade talks.

Both sides say no final figure will be agreed on Britain’s exit settlement next week. Significantly the UK plans to avoid a lump-sum settlement and will instead develop a system for regularly calculating payments in years to come, when specific liabilities are due.

Under this model, pensions of EU officials, for instance, could be paid on the basis of annual costs, meaning there will be no final figure for the so-called “Brexit bill” until the final eligible EU pensioner is dead, many decades from today.

The political compromise engineered between London and Brussels aims to guarantee to the other 27 EU member states that there will be no Brexit gap in the discharge of the current EU budget, while allowing the UK to point to much lower estimates of net payments and contingent liabilities.

Mrs May won the backing of her cabinet to break the deadlock in Brexit talks with an increased financial offer, but on the condition it was tied to a good trade agreement. British ministers have made clear that “nothing is agreed until everything is agreed”.

The prime minister’s original offer in her Florence speech in September covered about two years of transition payments, worth approximately €20bn in net terms. She added that Britain would meet other commitments, but until now had not clarified what that covered in discussions with the EU.

Since the start of talks, the main objective of the EU side has been for the UK to commit to meeting its share of gross EU liabilities accrued while Britain was a member state. A payment schedule for this “global settlement” would then be fixed in the second phase of talks.

According to commission estimates circulated to member states, these include €582bn of unpaid spending commitments in the 2014-20 long-term budget, about €83bn of obligations such as pensions and about €88bn of contingent liabilities, such as outstanding loans.

If a 13 per cent share is applied, as the European Commission initially estimated, Britain’s gross share comes to about €100bn.

Several EU diplomats told the Financial Times the UK had said to commission negotiators that it was willing to honour this full range of commitments under an agreed payment mechanism. France, Germany and other member states appear satisfied by the broad outlines of the deal.

UK estimates of its net share would take account of receipts worth about €28bn, including agricultural payments to UK farmers and structural funds for investment projects in Britain. Actual payments for structural funds could be made years from now.

British officials are working on other potential methods to bring down the net estimate, which the EU originally put at about €60bn. This includes using a higher rate for cancelled investment projects, the receipt of €3.5bn of UK capital at the European Investment Bank — potentially decades from now — and the payment of Britain’s 2018 budget rebate.

The mechanism for determining payments, once applied in future years, may take into account the fall of the pound and the decline in the relative size of Britain’s economy, thereby reducing the UK’s share from 13 per cent.

A spokesman for the Department for Exiting the European Union said: “Intensive talks between the UK and the European Commission continue to take place in Brussels this week as we seek to reach an agreement.

“We are exploring how we can continue to build on recent momentum in the talks so that together we can move the negotiations onto the next phase and discuss our future partnership.”

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