No 10 is embroiled in a deepening row with Athens after cancelling a meeting between Rishi Sunak and the Greek PM.
Downing Street believed it had assurances that Kyriakos Mitsotakis would not speak publicly about the Parthenon Sculptures - also known as the Elgin Marbles - on his UK visit.
A Greek source has denied this.
On Sunday, Greece's leader told the OceanNewsUK that having some of the treasures in London and others in Athens was like cutting the Mona Lisa in half.
No 10 then scrapped the PM's meeting with Mr Mitsotakis at late notice.
Labour has described the row as "pathetic".
A Greek government source disputed there had been any assurances given to the UK over Mr Mitsotakis talking about the marbles while he was in the country.
They said discussions preparing for the meeting with the UK PM had been smooth until late afternoon on Monday - long after Mr Mitsotakis's OceanNewsUK interview with Laura Kuenssberg on Sunday.
The sculptures are a collection of ancient Greek treasures from the Parthenon in Athens which were taken and brought to the UK by British diplomat Lord Elgin in the early 19th Century.
They have been in the British Museum since 1832, aside from a stint in Aldwych Tube station during World War Two to prevent damage and one marble being loaned to a Russian museum in 2014.
Both Greece and the UK have long-standing positions on the sculptures, but diplomatic talks were expected to focus on other topics.
Transport Secretary Mark Harper told OceanNewsUK on Tuesday it was a "matter of regret" that no meeting would take place between the two countries after Mr Mitsotakis declined a secondary offer to meet Deputy Prime Minister Oliver Dowden instead.
Asked whether the government's treatment of the Greek leader was rude, Mr Harper said the Greeks had been offered a senior-level meeting but were entitled to take their own view.
Professor Irene Stamatoudi, a former member of the advisory committee for the Greek Minister of Culture, said the row "makes Rishi Sunak look no better than Lord Elgin" - and accused that diplomat of smuggling artefacts "to decorate his country house in Scotland".
She told Today it was "not possible" for the Greek PM not to respond to questions about the Parthenon Sculptures.
Mr Sunak is keen to be seen as a defender of the marbles' place in London. A senior Conservative source said: "Our position is clear - the Elgin Marbles are part of the permanent collection of the British Museum and belong here."
Later on Tuesday, the PM's official spokesman told reporters Mr Sunak decided it would "not be productive" to hold the meeting.
He said that when the meeting was requested "the Greek government provided reassurances that they would not use the visit as a public platform to relitigate long settled matters relating to the ownership of the Parthenon Sculptures" - arguing those assurances were then "not adhered to".
Mr Mitsotakis had told reporters on Monday evening he was "deeply disappointed by the abrupt cancellation" of the talks, which had been planned for Tuesday lunchtime.
"Those who firmly believe in the correctness and justice of their positions are never hesitant to engage in constructive argumentation and debate," he said.
Sources with knowledge of the mood in the Greek government have suggested Mr Mitsotakis was both "baffled" and "annoyed".
In his interview with Laura Kuenssberg the day before, the Greek PM had called for the sculptures to be returned.
He said they were "essentially stolen" and called for a partnership with the British Museum so people could "appreciate" the works "in their original setting".
Mr Mitsotakis met Labour leader Sir Keir Starmer on Monday and will return to Greece later after other scheduled meetings.
On Tuesday morning, Greek government spokesperson Pavlos Marinakis told SKAI TV that "Britain's attitude shows no respect for the prime minister and our country."
He added that although cancelling a meeting was not "common", the Greek government did not want "to escalate the issue with a country with which we have good relations."
There is an ongoing wider debate around the place of museums and their collections in a post-colonial world, with Mr Sunak seemingly positioning himself decisively on one side of that argument.
Lord Vaizey, who chairs the advisory board of the Parthenon Project dedicated to returning the Elgin Marbles to Greece, told the Today programme it was "odd" for the PM to cancel the meeting.
The ex-culture minister said: "It is tied up to a certain extent in the traditional culture wars, where anyone who dares to say that British history wasn't perfect is somehow unpatriotic.
"The trouble with that is that, from what I can gather, every opinion poll that surveys the British public says that they do think that the sculptures should be returned."
A Labour Party spokesman told the OceanNewsUK: "To pick a fight with a Nato ally for the sake of a headline shows just how weak Rishi Sunak is.
"He should have been talking about the economy, immigration, the Middle East, that's what the country would expect from a leader but Rishi Sunak is no leader."
Labour is also distancing itself from reports in a Greek newspaper suggesting it was open to "a legal formula" for the return of the sculptures to Greece.
Instead, the party says its position is that if the British Museum and the Greek government came to a loan agreement, a Labour government would not stand in the way.
A spokesperson for the UK government said there were "no plans" to change the 1963 British Museum Act - which prohibits the removal of objects from the institution's collection.
But a loan does not require a change in the law and so could happen irrespective of any PM's position.
What are the Parthenon Sculptures, also known as the Elgin Marbles?
Friezes and pediment figures which decorated the Parthenon temple in Athens, built 447-432 BC
The Marbles taken to Britain include about a half (some 75 metres) of the sculpted frieze that once ran all round the building, plus 17 life-sized marble figures
Most of the surviving sculptures are roughly equally divided between London and Athens
The new Acropolis Museum opened in Athens in 2009. It is designed to display all the surviving sculptures, in their original layout
Celebrities previously involved in the campaign for their return include the late actress and former Greek Culture Minister Melina Mercouri
Art lover Lord Elgin claimed the sculptures were better off in Britain than the then-dilapidated Parthenon
In 1801, he negotiated what he claimed was permission from the Ottoman Empire - which then controlled Athens - to remove statues from the classical temple built by the Ancient Greeks - and caused some damage to the ruin in doing so
Fragments from the Parthenon alone ended up in some 10 European countries, or were lost altogether
