Britain will have to pay into the EU budget up until 2020 if it wants Europe to grant the UK reasonable terms on a Brexit transition deal, senior sources in Whitehall have told The Telegraph.

The idea, which is being actively discussed by British Brexit negotiators, would require a softening of British negotiation red lines in order to buy leverage and political goodwill in talks with the EU over a future trade deal.

Britain’s departure from the EU will leave a €10bn black hole in Europe’s finances which is causing significant anxiety in chancelleries across Europe, including in Berlin, which fears it will have to pick up the bill for any shortfall.

The immediate headache for Europe will be healing the gap between Britain’s departure in March 2019 and the end of the current seven-year budget framework which ends in 2020. British contributions to healing that gap could cost some €17bn euros.

“Payments up to the end of this MFF [Multi-annual financial framework] is something that we could put on the table which would help them fix a big short-term problem in their budgets,” said the source with firsthand knowledge of the UK pre-negotiation deliberations.

However the payments would be only be offered “in exchange” for a “sensible” EU offer on a transition deal – or what Theresa May has called an “implementation phase” – that both sides envisage will be needed for at least two years after Brexit day in March 2019.

The senior Whitehall source added that the UK side had also not ruled out “ongoing payments” of some kind, in exchange for a Free Trade Agreement (FTA) which is expected to take some time to negotiate and ratify after Brexit itself.

The ideas, which are highly sensitive given the likelihood of domestic political opposition from some hardline Brexiteers in Westminster, reflect a growing recognition on the British side that money will provide key leverage in the coming talks .

It comes as Jean-Claude Juncker, the president of the European Commission and Michel Barnier, the EU’s chief Brexit negotiator, arrive in London on Wednesday for face-to-face talks with Theresa May who will hold a dinner for the two in Downing Street.

At the same time Boris Johnson make his first speech of the election campaign, in which he is expected to say Britain will not turn its back on the World after Brexit.

Mr Davis, the Brexit Secretary, will also make a speech about the Government’s plans to make a success of Brexit, striking an upbeat note despite a stream of tough signals emanating from Brussels.

The European side has been hardening its lines on Brexit since Theresa May triggered Article 50 last month, and is making a transitional arrangement contingent on continued budget payments, free movement of people and accepting the jurisdiction of the European Court of Justice (ECJ).

The EU’s negotiating guidelines, which are to be finalised at a European leaders’ summit on Saturday, have also been toughened to include further expanded financial demands, including direct agricultural payments.

On trade, the latest draft includes a demand France to separate the key area of financial services from any trade deal, unless the UK agrees to become a rule-taker from Brussels and accept the EU’s “regulatory and supervisory standards regime”, Bloomberg reported.

Germany and France are leading demands not to backslide from Europe’s €60bn “Brexit bill” which has already drawn an outraged reaction from leading Brexiteers.

The prospect of paying significant sums to buy access also risks opening up cabinet splits, with David Davis, the Brexit secretary, taking a hardline on financial payments, according to EU diplomatic sources.

On a recent visit to an EU capital Mr Davis was continuing with a “confrontational” approach, telling his counterpart that Britain would not pay “a penny” after the UK’s departure in March 2019, or a Brexit “bill” but would consider paying for market access.

Charles Grant, the director of the Centre for European Reform, a pro-EU think-tank said that Germany – egged on by France – was leading the hardline on the budget issue, which Europe says must be satisfactorily resolved before it will agree to trade talks.

“Some top officials suggest that they will not compromise on the €60 billion,” he said, “But if the British are willing to compromise on the money, they will find the 27 willing to start talks on an FTA.

“They will also convince the rest of the EU that they are serious about reaching a mutually-beneficial de‎al, and that will help to create the goodwill that the UK requires in order to achieve generous access to the European market.”

In Brussels, senior EU sources said that substantive talks on financial matters had yet to begin with the UK, but warned that Europe would seek to separate Britain’s “legacy” owings from any payments related to the future EU-UK relationship.

The EU side has concerns that any early agreement on UK financial liabilities might be subject to revision when the crunch-point comes in the talks, likely in October next year, but does not deny the ultimate linkage between payments and trade access.

Some EU members states, such as Netherlands and Denmark are taking a softer line, according to EU sources, but they are being overruled by France, Germany and poorer countries, like Poland, which are determined to extract maximum cash from Britain.

For British negotiators, the concern is principally about selling the idea of making substantial payments to the British parliamentarians and public.

“Everyone knows there are large commitments and that Britain is a country that pays its bills,” said a second Whitehall source also involved in preparations for the talks, “It’s a question of coming up with a methodology that can be defended at home.”

Mrs May, who will make the final decision on any British offer, has been careful not to make any cost-iron declarations on the question of budget payments.

In a BBC interview after triggering Article 50, she hinted that the UK would be prepared to make substantial payments – but was clear they would not be characterised as an exit ‘bill’ or a payment for leaving.

“I am very clear about what the people here in the UK expect but I am also clear that we are a law abiding nation we will meet the obligations we have,” clearly hinting at the trade-offs involved.

In her letter to Mr Tusk, Mrs May acknowledged that the UK had “obligations” to Europe, but was also clear that these would have to be balanced against the UK’s “rights” as a departing EU member state.

She added that there would also be some “particular programmes” that the UK would pay to join because it was in the UK national interest.

Prominent remain supporters like Peter Mandelson, the former EU trade commissioner, have argued that Britain should “bite the bullet” and pay the full €60bn euros – a figure he described as “small change” when set against UK annual GDP.

“Britain is not one of those countries that doesn’t pay its bills, for good reason not least the impact it would have on the markets and market confidence in our future debt-raising,” he told an audience at the Institute for Government earlier this month.