Theresa May will tell EU leaders there is a shared responsibility to make Brexit work “smoothly” as she attempts to break the deadlock in negotiations.
In a major speech in Florence on Friday, she will say history will judge Brexit “not for the differences we faced, but for the vision we showed”.
The BBC understands she will propose a two-year transitional deal, after March 2019, ahead of a permanent trade deal.
It could include payments worth 20bn euros over the two years.
According to pre-released excerpts from her speech, the prime minister will say that a successful final agreement is in the interests of both the UK and the remaining EU countries.
“If we can do that, then when this chapter of our European history is written, it will be remembered not for the differences we faced, but for the vision we showed; not for the challenges we endured but for the creativity we used to overcome them; not for a relationship that ended but a new partnership that began.”
She is expected to say, if the UK and EU can be “imaginative and creative” about establishing a new relationship, both sides can be “optimistic about the future”.
Mrs May will argue that it is “in all of our interests for our negotiations to succeed… so I believe we share a profound sense of responsibility to make this change work smoothly and sensibly, not just for people today but for the next generation who will inherit the world we leave them”.
The view from Brussels
By the BBC’s Adam Fleming
Politicians and officials across the EU will listen to the tone of Theresa May’s speech but they mostly care about the content and its effect on the Brexit talks.
The UK’s offer to pay its membership fees until the end of the seven-year budget cycle is more generous than Britain’s pitch at the last round of talks but less than Michel Barnier wants.
And the media has paid little attention to the impasse over citizens rights, where the EU fears its nationals will have to go through an unacceptable administrative process to stay in the UK after Brexit.
Diplomats point out that talk is fine but the negotiations advance on concrete proposals, written down in legalistic documents.
Brussels officials are also gripped by the political situation in the UK, with one senior figure suggesting the prime minister is too weak to offer anything big and might not even be in her job in two weeks’ time.
They are open to a transition deal but the further it deviates from EU membership, the harder it will be to negotiate in the limited time available.
The BBC understands the prime minister will make what has been described as an “open and generous” offer, potentially worth 20bn euros over the two years – which could plug a black hole in the current EU budget, which runs to 2020 – created by the UK’s departure.
Mrs May briefed her top team at a marathon two and a half hour cabinet meeting in Downing Street on Thursday on what she will say in Florence.
A government source said that the intention was to make the potential payments conditional on continued access to the single market and some form of customs union which allowed the UK to strike its own trade deals during the transition period.
Mrs May is not expected to say exactly how much the cash offer will be worth, the exact nature of the arrangements for accessing the single market or any conditions attached to the money in her much-anticipated speech, as these are subject to the negotiations in Brussels.
Additional long-term liabilities, like EU pensions and debts, will also have to be dealt with in the talks to come, so the eventual Brexit bill is likely to be far higher than that 20bn euros (about £18bn).
The prime minister is also expected to repeat her assertion that the UK will seek its own bespoke trade deal after Brexit with the rest of the EU.
In a speech to the Italian parliament on Thursday, the EU’s chief Brexit negotiator Michel Barnier said that striking a deal with the UK was “in our common interest” but that only a year remained to come to agreement on the key issues – as six months would be needed for ratification before March 2019.
Mr Barnier said he was awaiting “clear commitments” from the UK on the issue of guaranteeing EU citizens’ rights, on the financial settlement and on the Northern Ireland border. Without those issues being resolved in a withdrawal agreement, there would be no transition deal, he said.
The fourth round of Brexit negotiations begins on 25 September, with the UK due to leave the EU in March 2019.