British and EU negotiators have reached a deal over the so-called Brexit bill, opening the door to a potential breakthrough in the talks this December, the Telegraph has learned.

Sources on both sides confirmed that an agreement-in-principle has now been reached over the EU’s demand for a €60bn financial settlement ahead of a crucial lunch meeting next Monday between Theresa May and Jean-Claude Juncker, the European Commission president.

Two sources confirmed that the terms were agreed at a meeting in Brussels late last week after intense back-channel discussions led by Oliver Robbins, the UK’s chief Brexit negotiator.

The Telegraph understands that the final figure, which is deliberately being left open to interpretation, will be between €45bn and €55bn, depending on how each side calculates the output from an agreed methodology.

It means the final amount will be far higher than the opening €20bn offer to win "sufficient progress" made by Mrs May in her Florence speech. The gross UK settlement, before deductions, is understood to be €100bn.

After being dragged down earlier in the day by Bank of England governor Mark Carney’s gloomy warning of potential Brexit “pain”, sterling spiked above €1.12 against the euro as traders piled into the currency on news of a breakthrough in negotiations.