Earl Spencer has apologised to Piers Morgan for incorrectly claiming in his new book about Diana, Princess of Wales, that the former tabloid editor was behind the publication of intrusive photos of the late royal in the mid-1990s.

Morgan had earlier threatened to sue Spencer over “fabricated inaccuracies” and “examples of brazen falsity” in the book, which was published on Tuesday.

In the memoir, the earl claims Morgan was in part responsible for the publication of photographs taken by an allegedly hidden camera in a gym, of Diana working out in a leotard.

But the broadcaster told his audience on YouTube on Monday that the pictures were published in the Sunday Mirror nearly two years before he became editor at the Daily Mirror and when he was working at the Sun.

Later on Tuesday, Spencer issued a statement apologising to Morgan and admitting he had incorrectly assumed Morgan had been editor of the Mirror at the time.

“Earl Spencer’s account of his conversation with Piers Morgan is accurate.

“Morgan was surly and annoyed when Earl Spencer called personally to tell him that he was not welcome at his sister’s funeral,” the statement said.

“The book then records Earl Spencer’s assumption that Mr Morgan’s response was because he was editor of the Daily Mirror when the Mirror Group had published highly intrusive photographs of Princess Diana at the gym.

“The photographs were published by the Sunday Mirror on 7 November 1993. Mr Morgan has pointed out that he did not join the Daily Mirror until October 1995. As an historian, accuracy is important to Earl Spencer. He therefore wishes to clarify that his assumption was incorrect. Earl Spencer apologises to Mr Morgan for this error.”

Morgan doubled down on his threat of legal action, writing on social media: “Earl Spencer has apologised to me for his defamatory lies published in his new book, Swan Song, published today.

“But I am pursuing legal action against him and his publisher Penguin to have the lies removed, and damages paid to the King’s Trust.”

The earl has made a series of claims in Swan Song: Diana, My Sister, including that King Charles said “we’ll forget her soon enough” after she died, which has prompted a war of words between him and Buckingham Palace.

The book also contains allegations about Morgan, who has strongly rebuked the claims.

Speaking earlier on his YouTube show, Piers Morgan Uncensored, Morgan said: “Many allies of his majesty have called into question these facts, ever since the most salacious accusations were serialised by the Daily Mail.

“Many royal commentators and experts have lined up to say that they simply don’t ring true. The king himself issued a furious rebuke that is almost without precedent. But, in essence, this has all been about opinions. Recollections may vary, after all. Well, until now.

“Because I can exclusively reveal on Uncensored that Earl Spencer’s book contains fabricated inaccuracies which will strike to the heart of his credibility. Spencer recounts how he personally called round the tabloid newspaper editors to uninvite them from Princess Diana’s funeral, after they had all been invited. I remember this well, because I was one of them.”

Morgan read an extract from Spencer’s book, which claims the editor “snarled with annoyance before he hung up”, as well as the passage concerning the intrusive photographs.

He told his audience on YouTube that the pictures were published in the Sunday Mirror nearly two years before he became editor at the Daily Mirror.

He said: “Well, this is all pretty extraordinary stuff, isn’t it? And very damning, particularly about me. I come across in the most despicable manner imaginable. There’s just one problem. It’s all bullshit and very, very easy bullshit for me to prove it.

“The photographs which he says that I published were printed by the Sunday Mirror on 7 November 1993. I joined the Daily Mirror in October in 1995. In fact, at the time of the gym pictures, I was doing a showbiz column on the Mirror’s arch-rival, the Sun. About as far removed from responsibility for the Mirror scoop as I could possibly have been.”

Morgan, who was the editor of the Mirror from 1995 to 2004, continued: “Earl Spencer was estranged from Diana and living in South Africa at the time of her death. As editor of the Daily Mirror, I had lunch with her at Kensington Palace with Prince William. After that, it wasn’t uncommon for her to call my office or for me to run stories by her … Ironically, by that time in her life I think I was probably talking to her more often than he was.

“My question, though, is this: if Earl Spencer can be so incredibly, defamatorily wrong about such basic facts involving me, well, why should we believe anything else he puts in this book?”

He later added: “In the meantime, Earl Spencer, you’ll be hearing – and your publishers – from my lawyers.”

Bookshops across London were reported to have appeared quiet on the release day of Spencer’s memoir – with the £28 book marked at half its cover price in some stores.

Dozens of copies with red “half price” stickers were stacked in Waterstones flagship Piccadilly store – the largest in Europe. It is also marked as half price on the Waterstones website.