Kate is “doing well” following her cancer diagnosis, Prince William has said.

The heir to the throne gave the update on his wife’s health on his first visit to the Isles of Scilly since becoming the Duke of Cornwall.

Tracy Smith, administrator at St Mary’s Community Hospital in Hugh Town, greeted William when he arrived and hosted his tour of the small medical centre following his visit to the harbour where he bought his entourage Cornish pasties.

Ms Smith said: “I asked William about his wife Kate and he said: ‘She’s doing well, thanks,’ and I suggested they might like to come for a visit and bring the children.”

William was given a card for his father the King – also a cancer patient – and Kate by Matron Lynda McHale, who said: “It was a card from my granddaughter who wanted to wish his father and wife ‘get well soon’.”

Kate revealed she was undergoing cancer treatment in a video statement in March.

The Duchess of Cornwall said of her diagnosis at the time: “This of course came as a huge shock, and William and I have been doing everything we can to process and manage this privately for the sake of our young family.

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“As you can imagine, this has taken time. It has taken me time to recover from major surgery in order to start my treatment.

“But, most importantly, it has taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be okay.”

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As the duke, William receives an income from the Duchy of Cornwall – a portfolio of land, property and investments – which owns much of the Isles of Scilly and nearly a third of residential buildings.

During his visit to the archipelago, the prince treated his staff to a round of Cornish pasties from the harbour cafe.

Asked what type he wanted, William replied “traditional”, and asked for five.

As everyone in the cafe laughed, he quickly added: “They’re not all for me.”

He added: “It does smell delicious in here.”

He also donned a wet suit to go swimming in the waters around Tresco – where it is rumoured he spends breaks with his family.

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