UK Prime Minister Andy Burnham suggests possible future referendum on EU rejoin

U.K. Prime Minister Andy Burnham suggested this week that British voters could be given the chance to reverse Brexit, the country's highly contentious departure from the European Union a decade ago.

Burnham, who became prime minister over the summer, told the BBC on Wednesday it was "possible" a referendum on rejoining the EU could be included in a future election manifesto.

A U.K. general election is not currently expected before 2029. Prime ministers are able to trigger an early snap election with the backing of parliament, but Burnham — who replaced predecessor Keir Starmer without a public vote — has ruled out such a move.

In his interview with the BBC, the prime minister said a referendum "wouldn't be the right thing to do right now," but added that the U.K. must "consider the options" for its relationship with the EU, arguing that "where we aren't good enough."

Asked whether an in-out referendum in a future election manifesto was a possibility, Burnham said: "yes, things are possible."

During the previous general election — which saw Starmer lead the governing Labour party to a landslide victory and end 14 years of Conservative rule — Burnham was serving as Mayor of Manchester. As he prepared to challenge Starmer's leadership, Burnham pledged not to "re-run" arguments over Brexit.

In a separate interview with the BBC's Today program, Burnham said he wanted to "look at the options" for resetting U.K.-EU relations.

"We could stay as we are. That's definitely an option, if people think this is the right place to stay," he said, when asked if he wanted Britain to rejoin the union. "We could look at what [former finance minister] George Osborne has said about a customs union, we could look at… the single market or we could go all the way."

The interviews came after Burnham's speech at the governing Labour party's annual conference on Tuesday, in which he said "Brexit hasn't given us control."

The 2016 Brexit campaign promised to "take back control" of immigration, free up more money for the country's health service, and forge trade deals with the rest of the world.

While the value of U.K. goods and services exports has grown significantly in the last decade, according to government figures, immigration and NHS funding pressures are more contentious than ever.

"Later this year, there will be a U.K.-EU summit," Burnham said at the conference on Tuesday.

"We will not give Britain the clear path we need into the rest of the century until we decide on a long-term relationship with what is still our largest market. I cannot say to you truthfully that where we are is good enough. Brexit has done more harm than good [and] we need to restore a higher level of growth and prosperity for Britain."

James Smith, developed markets economist at ING, told CNBC that while Burnham's statement is politically significant, unlocking tangible economic upside relies on concrete changes to the trading relationship, which could take years.

"Though the PM has opened the door to full EU membership, the reality is that he faces the same constraints that have hemmed in previous leaders," he said in an email. "The public may agree that Brexit hasn't gone well, but it's not clear there is a majority in favor of rejoining. It's also not at all clear how willing the EU will be to give ground in negotiations, given the recent volatility of U.K. politics and the possibility of a Reform-led government in the future."

Smith noted that it had taken more than five years to go from referendum to new economic relationship with the EU.

"I suspect it will take much longer for Britain to settle on and implement a new form of relationship now that [Brexit] has dropped down the list of political priorities among voters," he said.

Steve Nolan, a senior lecturer in economics at Britain's Liverpool John Moores University, told CNBC on Thursday that some estimates suggest U.K. gross domestic product was 5% to 8% smaller than it would have been without the vote to leave the EU.

"This hasn't been a surprise to economists — standard models in trade say that if you put up barriers to trade with your nearest trading partner then this will cause problems," he said. "So there are definite benefits to be reaped by rejoining, but the road towards that outcome could be rocky."

Any new referendum would increase uncertainty and turmoil, he added.

"The U.K. would also be asking to be let back into the club from a weakened bargaining position and may have to accept many conditions — [such as] euro membership and free movement of labor — that may cause economic and political difficulties. So, there are opportunities to grabbed, but they won't come without a cost."

However, Nigel Green, CEO of London-based financial consultancy DeVere Group, said that while closer ties with Europe would make Britain richer, it would also make it easier for capital to leave the country.

"Sterling stands to gain from a steadier relationship with the U.K.'s biggest trading partner, and U.K.-focused equities, priced at a discount for a decade, could start to close the gap," he said.

But he cautioned that "an open door works both ways," with entrepreneurs, and senior professionals increasingly telling deVere they were considering leaving the U.K. to avoid the high tax burden.

"The EU reset needs a domestic twin: competitive taxes, faster planning and policy stability that lets businesses look beyond the next Budget," he said. "Get both right and the U.K. becomes a magnet for capital in Europe. Get only one right and Britain becomes a more convenient place to leave."