The British Museum chairman has pledged to continue working on an exchange deal to allow the Elgin Marbles to be displayed in Greece despite a diplomatic fallout sparked by Rishi Sunak.

The Prime Minister scrapped a planned meeting with his Greek counterpart Kyriakos Mitsotakis after accusing him of grandstanding about the return of the ancient artefacts.

But George Osborne, chairman of the London museum where the friezes are on display, said he was pressing on with negotiations on the marbles, also known as the Parthenon Sculptures, “whether or not Rishi Sunak meets the Greek Prime Minister”.

Mr Osborne, a former Conservative chancellor, said it was clear from events this week that Mr Sunak’s administration would not support an exchange.

And we can go on doing it whether or not Rishi Sunak meets the Greek Prime Minister or not

But he said the stance taken by Opposition leader Sir Keir Starmer – who met Mr Mitsotakis in London this week – could pave the way for it to happen under a future Labour government.

A spokesman for Sir Keir has said his potential premiership would “not spend any time legislating on this matter” but that it “wouldn’t stand in the way” of a mutually beneficial agreement between the museum and Athens.

The 1963 British Museum Act prohibits the removal of objects from the institution’s collection, a position in law that Mr Osborne said would ensure Greece would have to return the sculptures following any exchange.

The debate over the Elgin Marbles has reignited this week following a diplomatic spat caused by Mr Sunak opting to cancel talks with Mr Mitsotakis at the “11th hour” after accusing him of reneging on a promise not to campaign for their return while in Britain.

No 10 said the Prime Minister felt reassurances were broken after Mr Mitsotakis used a BBC interview on Sunday to compare the current situation with the marbles to the Mona Lisa painting being cut in half and displayed separately.

Greece has long demanded the return of the historic works, which were removed by Lord Elgin from occupied Athens in the early 19th century when he was the British ambassador to the Ottoman Empire.

Part of friezes that adorned the 2,500-year-old Parthenon temple on the Acropolis, the Elgin Marbles have been displayed at the British Museum in London for more than 200 years.

The remainder of the friezes are in a purpose-built museum in Athens.

In comments made on his podcast Political Currency, Mr Osborne reiterated that he has “been exploring with the Greek government on behalf of the museum” an arrangement that would allow the sculptures to be displayed in Greece.

He told co-host Ed Balls he has been looking to reach a deal where the sculptures spend time in both London and Athens, with “Greek treasures coming our way in return”.

Mr Osborne continued: “And that is, I think, something worth exploring.

“And we can go on doing it whether or not Rishi Sunak meets the Greek Prime Minister or not.

“In fact, if anything, things have been rather clarified by this week. We obviously know we’re not going to get any particular support from the Conservative Government.

“But in fact the Labour leader, Keir Starmer, also said that while he supported the British Museum’s efforts, he wasn’t planning to change the law.

“And if you don’t change the law, then there is no prospect anytime soon of them just being restituted to Greece, returned with nothing, simply handed back, which anyway wouldn’t be a decision for the museum.

“And so to my mind, as chair of the British Museum, it is all the more reason to press on with our efforts to try and reach an agreement with the Greeks.”

On Thursday, Mr Sunak attempted to draw a line under the row despite only a day earlier in the Commons accusing the Greek leader of grandstanding over the marbles and trying to “relitigate issues of the past”.

The Prime Minister, quizzed by broadcasters during a visit to Guildford, insisted he was focusing on issues that mattered to voters and refused to say more on the row which has soured relations with an international ally.