In an exclusive BBC interview, Prince Andrew delivered a tense, sometimes bizarre denial of ever bedding his pal Jeffrey Epstein’s sex slaves — claiming his royal disdain for hugging, and his body’s inability to sweat due to a war injury prove he’s telling the truth.

“There’s a slight problem with, with, with, with the sweating,” Andrew told journalist Emily Maitlis, refuting an account by Epstein victim Virginia Giuffre, who has insisted that she was trafficked to the prince in 2001, after suffering his “sweating all over me” on a London dance floor.

Not true, Andrew insisted Saturday. “Because I have a peculiar medical condition,” Andrew told Maitlis.

“Which is that I don’t sweat, or I didn’t sweat at the time … because I had suffered what I would describe as an overdose of adrenaline in the Falklands War when I was shot at.

“And I simply — it was, it was almost impossible for me to sweat.

“And it was only because I have done a number of things in the recent past that I am starting to be able to do that again,” he added, apparently referencing sweating, but providing no further detail.

“So I’m afraid to say there’s a medical condition that says I didn’t do it.”

At another point, Andrew suggested that the now-notorious photograph of him standing with his arm around a teenaged Giuffre had been faked — because he’s not a hugger.

“I’m terribly sorry, but if I, as a member of the royal family, and I have a photograph taken — and I taken very, very few photographs — I am not one to, um, as it were, hug,” he stammered.

“Public displays of affection are not something that, that I do. So. That’s the best explanation I can give you.”

The interview, taped Thursday at Buckingham Palace — was a PR move so controversial, that Andrew’s newly-hired spin doctor, Jason Stein, quit after advising him not to go through with it.

Queen Elizabeth and Prince Charles — who only learned of the interview on the day it was taped — were also not amused.

“Charles thinks it is highly misguided,” a source told the Sunday Times of London of the interview.

In it, Andrew, 59, insisted repeatedly that he had “no recollection” of ever even meeting Giuffre, who has sworn in a 2015 deposition that the prince bedded her thrice, when she was 17 and 18, and at the behest of Epstein’s gal pal — and Andrew’s friend — Ghislane Maxwell.

There was that time in London in 2001, then again a few months later at Epstein’s Upper East Side mansion, and then again during an orgy on the Virgin Islands.

“To deny a recollection of Virginia in an interview is awfully weak and untested,” lawyer Stan Pottinger, who represents Giuffre, told The Post.

“If the prince will only accept our invitation to testify under oath we will be happy to refresh his recollection.”

Pottinger said that neither he nor his client were contacted by the BBC to respond to Andrew’s interview.

The prince also told the BBC’s Maitlis that he made a mistake in remaining friends with Epstein after the late financier was convicted of being a sexual offender in 2008.

Andrew even invited Epstein to the 18th birthday party that he threw for his daughter, Princess Beatrice — despite Epstein being the subject of an arrest warrant for the sexual assault of a minor at the time.

In an almost freakish apparent coincidence, rape-accused movie mogul Harvey Weinstein was also a guest, the Sunday Times of London reported.

Asked why he would still invite Epstein to his teen daughter’s party — a fancy dress affair at Windsor Castle —Andrew claimed he didn’t know then about Epstein’s criminal woes.

“At the time I don’t think I … certainly I wasn’t aware when the invitation was issued what was going on in the United States,” Andrew said.

He did admit, though, that his friendship with Epstein went on a bit too long.

“I stayed with him and that’s the bit that . . . as it were, I kick myself for on a daily basis because it was not something that was becoming of a member of the royal family and we try and uphold the highest standards and practices and I let the side down, simple as that,” the prince said in his televised interview.

A source previously told London’s Sunday Times that Andrew had traveled to New York City in 2010 to end his friendship with Epstein after the financier had served 13 months in a Florida jail for procuring an underage girl for prostitution.

“Andrew put his head in the sand about the Epstein affair for years, but it wouldn’t go away,” one royal source told The Post.

Surprisingly, the royal source added that Andrew had also considered sitting down for an interview with a US network, thinking they may be “more sympathetic.”

Maitlis, a veteran host of the BBC’s “Newsnight,” had been in talks with Buckingham Palace about an interview with the prince since May, a source told The Post, adding that Andrew obtained permission from the Queen and questions were not vetted in advance.

The prince finally agreed to sit down with the BBC, the source said because, “[he] felt he was backed into a corner. His reputation was damaged and he feared the impact this was having on the royal family.

“It was affecting his job — and you can’t resign from the royal family.”

The surprise interview came days after Andrew was given a spot front and center — near his mother, Queen Elizabeth, and between future king Prince Charles and Prime Minister Boris Johnson — as the royal family and other dignitaries gathered to mark Remembrance Day and mourn Britons who died at war.

It was yet another public show of the queen’s strong support of her third child. On the day after Epstein’s Aug. 10 death, she and a grinning Andrew were seen alone in a car leaving church.

“The queen is very protective of Andrew and always has been,” Ingrid Seward, editor-in-chief of Majesty magazine, told The Post. “We all say he’s the Queen’s favorite . . . and I think she does seem to be protecting him.”

As for why the Duke has so far declined to help US authorities in their investigation against Epstein, a royal source said: “Members of the royal family would always cooperate with the police in an appropriate way.”

Andrew could be subpoenaed in a number of civil court cases filed in the US and involving Epstein. Legal sources say that the prince could be compelled to give testimony either in a deposition or in a courtroom.

“Any place where Andrew is likely to be part of the story, he can be called as a witness,” Pottinger said. As a result, “I don’t think we’ll see him on this side of the pond any time soon.”

The Palace declined to comment on speculation that the royal could be called as a witness.

Andrew and Epstein were reportedly introduced in the 1990s by Maxwell. The trio became so close that, in June 2000, Epstein and Maxwell attended the Dance of the Decades, a massive celebration at Windsor Castle hosted by the Queen to mark Prince Andrew’s 40th, Princess Anne’s 50th, Princess Margaret’s 70th and Prince William’s 18th birthdays.

In the following years, Epstein and Maxwell were invited to shooting parties at Sandringham House, the Queen’s country retreat in Norfolk, and were said to have stayed at Balmoral, the Queen’s estate in Scotland.

In return, Epstein hosted the prince — nicknamed Randy Andy in his youth — at his Palm Beach estate and regularly at his Upper East Side mansion. Earlier this year, Sarah Ferguson, Andrew’s ex-wife, had to apologize for accepting a loan of about $24,500 from Epstein in 2010.

Andrew said in a previous statement that he stayed in “a number” of Epstein’s residences, but that he did not “see, witness, or suspect” any of the criminal behavior that led to Epstein’s June 2019 indictment.

“Virginia has never wavered in her story, she’s been consistent about this for years, whereas Andrew is all over the place,” lawyer Pottinger told The Post.

The scandal has even had an impact on the pending nuptials of Andrew’s eldest daughter, Princess Beatrice, to Edoardo Mapelli Mozzi, planned for next year.

A well-placed fashion source told The Post: “Beatrice wanted a very well-known British female designer to make her gown, but the designer gently turned her down as she felt the optics would not be great for her brand.”

The wedding is already set to be on a smaller scale than that of Beatrice’s younger sister, Princess Eugenie, who married Jack Brookbank at St. George’s Chapel at Windsor Castle in October 2018.

There were rumors in London circles that Andrew — always keen to ensure his daughters are treated as first-tier royalty — had originally wanted to use Westminster Cathedral for the wedding.

“Altogether, the Epstein scandal has really thrown a spanner in the works for the wedding,” an insider said.

The Palace would not discuss the wedding.

“Nobody knows what the fallout of this interview will be,” Richard Kay, editor-at-large of the UK’s Daily Mail newspaper, told The Post. He pointed out that other royal TV confessions — specifically by Princess Diana and Prince Charles — were conducted “with the best of intentions, but . . . now they are only remembered for both confirming they had committed adultery.

“For Andrew, the risks are 10 times higher, but I am told he felt that facing the public was the only thing he could do,” Kay added.

A Buckingham Palace spokeswoman told The Post: “There has been a great deal of continued speculation in the media about [Prince Andrew’s] former friendship with Mr. Epstein and the allegations which have been repeatedly denied with regard to Ms. Roberts [Giuffre]. HRH wished to address them clearly and publicly.”

No matter the fallout, Seward insists the likelihood of Prince Andrew ever testifying in any Epstein cases is slim.

“The royal family won’t allow a prince of the blood, the Queen’s second son, to be made to stand up in a court,” she said. “They’re not going to let it happen.”