The Duke of Cambridge has told his wife that losing their mother at a young age had brought himself and Prince Harry closer together – but the brothers conceded they had not talked enough about their mum.

Kate praised the royal siblings for coping with the “trauma” of Diana, Princess of Wales’ death in a car crash almost 20 years ago, partly attributing this to their amazing bond.

The royal brothers’ frank admission comes at the end of a week where the Cambridges and Harry have been discussing personal issues in their lives in a bid to encourage others to support their Heads Together mental health initiative, which aims to get the nation talking about their problems or listening to others.

The casually-dressed royal trio were filmed chatting around a bench in the grounds of Kensington Palace on Wednesday for a video released to highlight their Heads Together project.

William was 15 and his brother just 12 when their mother was killed in the car crash in Paris on August 31 1997.

Kate sympathised with their bereavement and said despite everything “you boys obviously sadly went through, the trauma that you experienced”, they had remained “strong” and had been able to “cope” because of childhood experiences and their close relationship.

The Duke told his wife: “But we have been brought closer because of the circumstances as well, that’s the thing. You are uniquely bonded because of what we’ve been through.

“But even Harry and I over the years have not talked enough about our mother.”

Speaking about himself and his brother, Harry told Kate: “Both of us have always been open to each other, we’ve never really talked about it, never really talked about losing a mum at such a young age.”

The prince has already revealed in a national newspaper interview how he spent nearly 20 years “not thinking” about his mother’s death and eventually got help after two years of “total chaos”.

When William said he and his brother Harry had not talked enough about their mother, Harry agreed, saying: “Never enough”, and when Kate asked if their Heads Together campaign had made Harry realise this, he replied: “Yeah, I think so.”

He added: “I always thought to myself, you know, ‘what’s the point of bringing up the past, what’s the point of bringing up something that’s only going to make you sad? It ain’t going to change it, it ain’t going to bring her back.’

“And when you start thinking like that it, can be really damaging.”

Mentioning William, he added: “You always said to me ‘you’ve got to sit down and think about those memories’, but to me it was like: ‘Don’t want to think about it.'”