THERESA May will today tell her fellow EU leaders that the hand of European history is on their shoulders and that they "share a profound sense of responsibility" to make Brexit work not just for people today but for future generations to come.

In a keynote speech in Florence aimed at unblocking the Brussels talks’ deadlock, she is expected to say that Britain is ready to make an "open and generous offer," suggesting a two-year transitional period from 2019, which would avoid a cliff-edge and offer certainty and clarity to businesses.

While no "divorce bill" figure will be mentioned, officials have privately been mooting one of around £17 billion, some 10 billion euros a year, to pay Britain's dues into EU coffers.

This will mean that no other member state will lose out as the UK undertakes its slow-motion withdrawal.

In return, the Prime Minister will expect Britain to get good access to the single market and some form of customs union during the two-year transition.

However, with the UK having to negotiate additional long-term liabilities such as contributing to EU pensions and taking a share of the bloc's overall debt, Britain’s eventual Brexit bill is likely to be far higher than the £17bn already mooted.

In what No 10 described as a speech setting out an “ambitious vision of a new partnership,” the PM will say: "The eyes of the world are on us but if we can be imaginative and creative about the way we establish this new relationship...we can be optimistic about the future we can build for the United Kingdom and for the European Union.”

And in a message to Britons fearful of life outside the EU, Mrs May will strike an upbeat note, saying: "Our fundamental strengths are considerable: a legal system respected around the world; a keen openness to foreign investment and enthusiasm for innovation; an ease of doing business; some of the best universities and researchers you can find anywhere; an exceptional national talent for creativity and an indomitable spirit.”

On the eve of the PM’s keynote speech, Michel Barnier issued a fresh warning to Britain that it must "settle the accounts" if it wanted a free trade deal with the EU post Brexit.

Speaking at the Italian Parliament, the EU’s chief negotiator said there was still "major uncertainty" over the UK's approach on key issues.

"All that is necessary in this negotiation is that everyone honours the commitments that they have made to each other; to settle the accounts; no more, no less," declared Mr Barnier.

"Beyond money, this is a question of trust between the 27 and the United Kingdom based on the respect of one's signature. Everyone knows that we will need this trust to create a solid relationship in the future," explained the EU chief negotiator.

Mr Barnier made clear he would be listening "attentively and constructively" to what Mrs May would be saying on Friday afternoon.

Early on Thursday, she briefed her colleagues in a marathon two-and-a-half-hour session of the Cabinet. Members got half an hour to digest the 5,000-word speech before they discussed it with the PM in the chair.

Just before lunch, senior ministers emerged into Downing Street. David Gauke, the Work and Pensions Secretary, declared: “We’re united and all behind the speech.”

In what appeared to be a choreographed show of public unity, Philip Hammond and Boris Johnson - who have been at loggerheads all summer over Brexit – left No 10 together; smiling.

Yet the difference of approach between the two Cabinet heavyweights appears difficult to bridge.

The Chancellor favours a Swiss-style deal in which Britain would continue to pay for access to the single market while the Foreign Secretary wants a looser arrangement along the lines of the EU's free trade agreement with Canada.

Mrs May sits somewhere in the middle, insisting it is not a "binary" choice and she would be seeking a "bespoke" arrangement for the UK rather than following a pre-existing, "off-the-shelf" model.

Mr Hammond and Mr Johnson together with David Davis, the Brexit Secretary, will be in the audience when the PM delivers her speech in Florence; chosen deliberately because of the city’s historic links to European trade and culture.

At home, the last few days have been dominated by a damaging row caused by the Foreign Secretary’s 4,222-word article on Brexit, which Ruth Davidson, the Scottish Conservative leader, denounced as ill-timed given the Parsons Green Tube bombing, and Amber Rudd, the Home Secretary, criticised as “back-seat driving” on Britain’s EU withdrawal.

As the prospect of the Foreign Secretary resigning was talked up and then talked down, Mr Johnson declared that he was “mystified” by the row. He dismissed it as a “snore-athon”.