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.

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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”.