Sarah, Duchess of York, is “all clear” and “doing really well” after recent health issues, her daughter Princess Beatrice has said in her first live television interview.

Beatrice appeared on This Morning on Monday, live from the top of the Empire State Building in New York, where she was launching a campaign with Outward Bound, a charity she supports.

Asked by presenters Craig Doyle and Josie Gibson about her mother, who has faced two recent cancer diagnoses, Beatrice said Sarah has “had a bumpy health scare last year” but has had the “all clear” and is “thriving”.

“She’s been through so much but I think, really, now she’s sort of coming into her own. I think we’re just reminded, when any parent or individual has sort of a health scenario, just really get the checks that you need to get as early as you possibly can.

“I think, you know, both my sister and I are so proud of her for taking those steps to get those checks and [we’ve] sort of really modelled our health considerations on that.

“We’re really lucky in the UK to make sure that you can get those checks as best you can and hopefully we can do as much as we [can] to support each other when anyone goes through a health scare.”

Later in the interview, she added: “Nothing’s more important than family.”

Sarah, 64, was diagnosed with breast cancer in June last year after a routine check-up, and underwent a successful single mastectomy operation. She then faced further concerns in January when she was diagnosed with malignant melanoma, a form of skin cancer.

She is one of three members of the royal family to have faced health issues this year, as the King and the Princess of Wales continue with treatment for undisclosed forms of cancer.

Charles returned to public engagements last week, while Kate continues to navigate her treatment privately.

Sarah sent her well wishes to Kate after the princess publicly announced her diagnosis in March, and said: “As someone who has faced their own battles with cancer in recent months, I am full of admiration for the way she has spoken publicly about her diagnosis and know it will do a tremendous amount of good to raise awareness.”