Prince Andrew thought his daughters were “obvious successors” to older royals when they gave up their official duties, according to a new book.

According to Sasha Swire, the wife of former MP Hugo Swire, the Duke of York, 60, thought Princesses Beatrice and Eugenie should be able to take on formal duties, rather than hold normal jobs as they do now.

Writing in her diary, which has been published and was serialised in The Times, Swire recalled meeting Andrew in 2011, at the point where the two princesses were having their security withdrawn as the Sovereign Grant was altered.

She wrote that he was “desperately concerned” about their royal protection going, because “they move around in the age of Twitter and instant messaging, and that an antagonistic force could be mobilised against them in minutes”.

Swire added: “He also says that there is a tier of royals currently doing official duties who will soon no longer be there on account of their age and Beatrice and Eugenie are their obvious successors. I am slightly astounded that anyone would even contemplate that role and ask: ‘Is that the life they really want?’ He says yes, it is.

“I sit silently but I’m thinking he might consider having a quiet word with them about taking part in a reality TV series with Fergie and disclosing their troubles on Oprah’s sofa, which doesn’t exactly chime with their princess status.”

Prince Andrew, Princess Eugenie, and Sarah Ferguson, with Catrina Skepper, Countess Guerrini-Maraldi, Dave Clark, Princess Beatrice and Jack Brooksbank at Royal Ascot in 2015. (Getty Images)

Beatrice, 32, and Eugenie, 30, both have full-time jobs, and don’t take on any duties on behalf of the Queen. They do have associations with some charities, but these are as private patrons, not as royal patrons.

Andrew has stepped back indefinitely from his duties, after a disastrous interview with the BBC about his friendship with Jeffrey Epstein.

The prince has denied allegations of having sex with Virginia Giuffre, who says she was trafficked by the disgraced financier Epstein when she was a teenager.

He has not been charged with any crimes, but has been caught in a war of words with US authorities who claim he has not co-operated with their investigation into Epstein despite promising to do so.

His website no longer exists, but he was given a page on the Royal Family website, which lists working royals.

Princess Eugenie, Prince Andrew, and Princess Beatrice at Harry and Meghan’s wedding in May 2018. (Reuters)

In 2011, Andrew’s former wife, Sarah Ferguson, appeared in a reality TV show in the US called Finding Sarah, which followed her rebuilding her life after royalty.

Princess Eugenie, then 21, appeared in the final episode alongside her mother, as Ferguson returned to the UK.

Princess Beatrice also appeared later in the same episode, shedding tears over her mother’s financial problems.

Beatrice and Eugenie are regular attendees at royal events such as Trooping the Colour, and are invited to Christmas with the Queen at Sandringham.

Ferguson no longer attends those events but still lives in the Royal Lodge in Windsor, with Andrew, although they have been divorced for several years.

During lockdown she shared a photo of her with Andrew and their daughters, and praised their “united” family.