Friends of King Charles and the Prince of Wales have rubbished claims of a rift between them in Endgame by Omid Scobie, an author close to the Duke and Duchess of Sussex.

Sources close to the 75-year-old monarch and his elder son have described how their relationship has improved since Harry and Meghan broke with much of the family and then quit to live abroad, although it is accepted that there are occasional tensions.

“The crisis over Harry and Meghan really brought them closer together,” said one. Another pointed to a Father’s Day photograph, taken by the Princess of Wales and released in June 2020 as the first outward sign signalling a strengthened relationship between the two men.

Taken the year before as the tensions deepened with Harry, it showed Charles resting his head on William’s shoulder while the son put his arm around his father. “It was no accident that it was released. These things don’t happen by accident,” one source said.

Staff at Buckingham Palace and Kensington Palace have been ordered not to fuel the fire over the book, which alleges that the future of the monarchy is in a crisis and a fight for its survival.

But privately some friends of the family have expressed outrage at Scobie’s portrayal of the monarchy, arguing that much of it is nonsense.

The claims over the King’s relationship with William have caused particular irritation, with the author citing a source saying: “William (doesn’t) think his father is competent enough, quite frankly. Though they share passions and interests, their style of leadership is completely different.”

Scobie portrays their relationship as fractious, writing: “Distrust and simmering animosity between father and son are nothing new to their working relationship.”

Yet aides of William and Kate have suggested in the past few months that one of the main reasons that the couple have not yet visited some of the King’s key Commonwealth realms, such as Australia and New Zealand, is respect for the monarch. While other royals such as Princess Anne and Prince Edward have been Down Under, the greater publicity that William and Kate attract has raised fears they might steal the monarch’s thunder because he has not yet visited the countries in the new reign.

The book accuses Kate of ignoring Meghan’s “cries for help” and more generally of being “cold” if she does not like someone.

Scobie, 42, writes: “This is a side of Kate that rarely gets written about. “Advocating for mental health causes – the mental health of mothers, for that matter – but ignoring her own sister-in-law’s cries for help seemed out of character for someone the public knew as sweet and easy to get along with.”

The author also claims that Queen Camilla is someone who “rolls her eyes” when subjects such as veganism or gender identity are mentioned.

Friends accept that Camilla, 76, is an ardent defender of freedom of speech and someone who makes jokes about political correctness. In February she criticised the rewriting of Roald Dahl’s books to avoid upsetting modern sensibilities on topics such as weight, gender, and mental health.

At her 75th birthday celebration with national treasures in July last year she joked: “Ladies and gentlemen, if I’m allowed to call you that.”

But 10 years ago, long before Harry and Meghan were meeting gender fluid young people at public engagements, the Daily Express watched as Camilla happily chatted, unfazed and charming, to a transgender person at the 75th anniversary of the Royal Voluntary Service at St Paul’s Cathedral in London.

Scobie’s book makes a series of unsubstantiated allegations that William and other family members “covertly sanctioned” leaks to reporters about Harry.

He also writes that Charles and Meghan exchanged letters in the wake of her interview with Oprah Winfrey. The alleged letters are said to reveal the identity of two people who Meghan claimed, in the TV interview, raised “concerns” about the colour of then-unborn Prince Archie’s skin.

In an embarrassment for the author and his publishers, copies of the book had to be withdrawn from sale in the Netherlands yesterday after it emerged that a senior member of the Royal Family had been named as one of the people who made the skin colour remarks.