Speaking to reporters on Thursday, Burnham was asked to explain if his decision to reopen the debate on the UK’s future with Europe had helped or hindered the negotiations linked to the summit.
Burnham replied “I think it has helped” before adding: “We’ve got a big week ahead of us to try and get this deal over the line.
“But let’s be clear what’s at stake: what we can achieve through this deal is lower prices for British consumers, lower costs for British businesses, more growth in our economy so there’s really big prizes here, and I will fight now over the days to come to make sure we get this deal over the line.”
Pressed on whether discounted university tuition fees for European students would be part of the deal, Burnham said “requests are coming from the European side, we are putting our requests on the table too”.
He added: “I believe there is a good deal to be done that could be a win-win for Britain and Europe. I think it actually could be more like the Brexit that people thought they were voting for in 2016.”
Ahead of the summit, the UK and EU agreed a draft deal on removing post-Brexit checks from food and agriculture exports.
Similar texts for deals on emissions trading and a youth travel and work scheme have also been circulated to EU nations.
As a result of the agreement, the government claims the UK economy will eventually see £5.1bn worth of annual benefits.
Burnham also told MPs last month that the summit presents an opportunity to make progress on “controlling illegal immigration”.
Conservative Party leader Kemi Badenoch has previously strongly opposed any move to align with EU rules, saying it would “actually take us backwards”.
On Thursday, Conservative MP and former minister Dame Priti Patel said: “Andy Burnham’s obsession with the EU risks dragging Britain backwards, damaging our economy and leaving hardworking British taxpayers footing the bill.”
The Liberal Democrats earlier this month described the draft deal as a “patch, not a fix” and said the “real solution is to re-join the single market and to establish a customs union with the EU”.
Reform UK believes one of the “key benefits” of Brexit is that Britain no longer has to “adhere to ridiculous EU rules” and any form of alignment could have a negative impact on the country’s trade policy.
The Green Party has called for the UK to re-join the customs union, with leader Zack Polanski previously saying “full membership of the EU remains the best option for the UK”.
