Andy Burnham believes a “win-win” deal with the EU is possible — one that could be “more like the Brexit that people thought they were voting for in 2016”.

The prime minister was meeting fellow leaders at the European Political Community summit in Dublin, ahead of a keenly anticipated EU-UK summit next week at which he hopes to bring Britain closer to Europe.

At the bilateral summit, the EU and UK hope to sign deals on food and drink, emissions trading and a youth mobility scheme. But tuition fees for European students remain a stumbling block.

Burnham said: “I believe there is a good deal to be done that could be a win-win for Britain and Europe.

“The deal is not done, and there’ll be some long nights ahead in the next seven days.”

He said the reset would be about whether we can “take a step back to closer working relationships with Europe”.

Burnham added: “We ended up with a far harder Brexit, I think, than people thought they were getting when they went to the polls.”

The EU has said the prized food and drink deal and emissions-trading agreement may not enter into force without an agreement allowing European students to pay domestic tuition fees.

Burnham said it was a package deal, but would not be drawn on whether he accepted that link.

“I’m going to be fighting hard for these benefits for Britain in the next seven days … they will make a real difference. If I can do anything to address the cost of living crisis, I should be doing it.”

He has previously said the food and drink deal, which would ease Brexit red tape, will add 0.4% to British GDP.

The prime minister also said David Cameron had been wrong to argue that Britain’s problems had “nothing to do with Brexit”, adding that there would be “long nights ahead” negotiating a reset with the EU before the summit.

Cameron, the prime minister who lost the 2016 Brexit referendum, told Bloomberg News that Burnham should not seek to bring Britain back into the EU. He argued that the UK’s problems had nothing to do with its exit from the bloc.

Asked about those remarks, Burnham said: “I think he is wrong to say that the low growth that we’ve had over the last decade has, quote, ‘nothing to do with Brexit’. I would say the evidence says otherwise.

“It feels like his intervention is more about unity in the Conservative party than it is about fighting for the British interests.”

Burnham has recently said he is open to rejoining the single market or customs union, or to “go all the way” by rejoining the EU. He said a deeper relationship would be the outcome of future talks, “and it will be in the outcome of that negotiation that then we will take a decision as a cabinet, on what, if anything, comes next”.

Earlier on Thursday, the EU foreign policy chief, Kaja Kallas, said she wanted to see Britain rejoin the EU, but warned that negotiations would not be easy after the “trauma” of the Brexit years.

She said: “I would very much like to see Britain back in Europe, but, of course, we also have in the European Union, a lot of, I would say, trauma from Britain leaving, so the negotiations will not be that easy.”