Theresa May has moved to dampen expectations of a breakthrough in talks as she arrived in Brussels seeking Brexit concessions from EU leaders.

The prime minister told reporters on the doorstep of the summit that she is not expecting an “immediate breakthrough” at the meeting, where she will try to convince the 27 other leaders to make concessions.

Ms May promised her mutinous MPs that she will try and get legally binding assurances on the controversial Northern Ireland backstop, but the EU has said the withdrawal agreement is not up for renegotiation.

The PM at Thursday lunchtime also declined to name a date for her departure, having pledged to her MPs last night that she would step down before the next election in 2022.

“It’s in the best interest of both sides, the UK and the EU to get the deal over the line, to agree a deal – but I recognise the strength of concern in the House of Commons and that’s what I will be putting to colleagues today,” she told reporters.

“I don’t expect an immediate breakthrough, but what I do hope is that we can start to work as quickly as possible on the assurances that are necessary.”

The PM reportedly told a meeting of her parliamentary party on Wednesday night that she would not commit to a deal that did not have legally binding assurances that the UK could end the backstop. She also pledged to leave office before the 2022 general election – essentially starting the clock on the next Tory leadership contest.

Asked whether she had a date in mind for leaving office, the PM said: “No, people try to talk about dates. What I’m clear about is the next general election is in 2022 and I think it’s right that another party leader takes us into that general election.”

Ms May met with Irish prime minister Leo Varadkar this morning, which he described as "very long", and is also having bilateral discussions with Luxembourgish PM Xavier Bettel and European Council president Donald Tusk.

She will try to convince EU leaders of the need to grant her concessions at a rare 28-way back-and-forth session this afternoon. After dinner the leaders will decide amongst themselves without Ms May what to offer her – they are expected to offer a written statement.

Arriving at the summit the other European leaders tempered expectations but said they were willing to help.

Juha Sipila, the Finnish prime minister told reporters that it would be “a little bit difficult” to give the PM legally binding assurances but that leaders wanted to try and help anyway.

“Legally binding will be a little bit difficult, but anyway, I think that we all want to help. First of all, our goal is that the new relationship will be made before the backstop,” he said.

“So I think at the political level we can say it again that that’s our primary call. Let’s see if we can find something from the legal side also, but it’s open still.

“This question is very important for all of us and we have to have some kind of solution in case there is no deal for the future relationship. This is the reason why this backstop is there but of course our primary goal is to find a solution for the new relationship also, so that we don’t need any backstops.”

Austrian chancellor Sebastian Kurz said: ”We are ready to accommodate Theresa May. It’s not about pushing through maximum positions but to find a provision that is the best possible for both sides.”

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“The deal itself is non-negotiable,” Dutch Prime Minister Mark Rutte said as he arrived in Brussels. “So today is about clarification.”

But powerful German chancellor Angela Merkel struck a less accommodating tone.

“I do not see that this Withdrawal Agreement can be changed,” she said on arrival.

“We can discuss whether there should be additional assurances, but here the 27 member states will act very much in common and make their interests very clear.

“This is always in the spirit that we will have very, very good relations with the UK after it has departed from the European Union.”