The Duke of Cambridge and the Duke of Sussex put on a “very good show” despite their rift, a royal author has said.

The brothers appeared together at the unveiling of a new statue of Diana Princess of Wales, described as “stunning” by Penny Junor.

She said William and Harry appeared relaxed with one another at the unveiling ceremony at Kensington Palace, but their troubled relationship was unlikely to have been fully resolved.

The royal writer, author of Prince Harry: Brother, Soldier, Son, Husband, said: “My guess is there’s quite a way to go, but it’s encouraging to see the two of them together, and with smiles on their faces. I think that is progress.”

The dukes unveiled the bronze monument to their late mother in the palace’s Sunken Garden on what would have been her 60th birthday.

Ms Junor said: “I think the brothers put on a very, very good show.

“I was expecting to see some sort of tight lips and some jaw muscles which we saw at the Commonwealth service in Westminster Abbey before Harry and Meghan left.

“They seemed to be reasonably relaxed with one another. They weren’t arms around each other, it wasn’t very touchy and there wasn’t, perhaps, the usual banter of times gone by.

“But had you not known there was a serious problem between the two of them, you wouldn’t necessarily have picked it up.”

Harry accused the royal family of racism in an interview with Oprah Winfrey and the institution of failing to support the Duchess of Sussex when she was suicidal.

Meghan also said the Duchess of Cambridge made her cry ahead of her wedding.

Harry went on to suggest in a podcast interview that Charles and the Queen and the Duke of Edinburgh had failed as parents.

His rift with William stretched back to before his wedding, with Harry angered at what he perceived to be his brother’s “snobbish” attitude towards his bride.

Ms Junor added: “William is protective on behalf of Kate and his father and his grandmother, and Harry really took a swipe at all of them.

“So it’s not just something between the two brothers, this is bigger than that.

“My guess is that William is looking for an apology. And whether he would accept that apology, I would hope he’s big enough to, but they are both stubborn individuals.”

She said of the statue: “I think it looks stunning. I love the fact that it’s larger than life. And I love the fact that she’s got three children with her.

“I like the fact she’s in ordinary clothes. It’s a good likeness.”