Andrew Mountbatten-Windsor and Peter Mandelson have been pictured in bathrobes alongside Jeffrey Epstein, in the first known photograph of them together.

The trio were captured relaxing outside at a wooden table with mugs decorated with the American flag in the newly unearthed photograph believed to have been taken on Martha’s Vineyard, an island off Cape Cod in Massachusetts that is favoured by the wealthy.

No date or location was given for the picture, which was part of the millions of Epstein-related files released by the US Department of Justice earlier this year.

But a similar photograph of Mandelson appeared in Epstein’s 50th birthday book from 2003, in which Mandelson called Epstein “my best pal”.

That picture shows Mandelson in a white bathrobe grinning opposite Epstein, who killed himself in August 2019 while awaiting trial on sex-trafficking charges.

The former ambassador to the US referred to Epstein as an “intelligent sharp-witted man” in a handwritten note in the book, which was last year provided to the House committee on oversight and reform, the main investigating committee in the US House of Representatives.

Mandelson and Mountbatten-Windsor feature multiple times in the Epstein files, including images of the latter bent over an unidentified female and lying across the laps of women, and photos of Mandelson in his underwear and receiving a foot massage.

There is no suggestion that appearing in the documents implies any wrongdoing.

Mandelson and Mountbatten-Windsor, the former Duke of York, have faced a public fallout over their relationships with Epstein, who was jailed for soliciting prostitution from a minor in 2008.

Mountbatten-Windsor was stripped of his titles and given notice to vacate the 30-room home in Windsor that he occupied on a peppercorn rent. He was arrested last month on suspicion of misconduct in public office over allegations he shared confidential material with the convicted sexual offender while serving as the UK’s trade envoy. Mountbatten-Windsor has always denied any wrongdoing.

Mandelson was sacked as the UK’s ambassador to Washington last September and resigned from the House of Lords in February over his ties to Epstein. He was arrested last month on suspicion of misconduct in public office over claims he allegedly leaked sensitive government information to Epstein while serving as business secretary in Gordon Brown’s cabinet.

Mandelson has denied any wrongdoing. His lawyers said last week he would cooperate with the police investigation.

Mountbatten-Windsor and Mandelson have both since been released under investigation.

Keir Starmer has faced scrutiny over his decision to appoint Mandelson as the UK ambassador to Washington. The prime minister apologised again on Thursday over his handling of the appointment, saying: “It was me that made a mistake, and it’s me that makes the apology to the victims of [Jeffrey] Epstein, and I do that.”

It came a day after 147 pages of documents relating to Mandelson were released by the UK government.