Kate doing well, William says, during visit to Isles of Scilly

The Prince of Wales has given a positive update about his wife’s cancer treatment – saying “she’s doing well”.

William was asked about Kate as he toured the only hospital on the Isles of Scilly to learn about a major building project to improve facilities being constructed on land owned by his Duchy 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.”

The Princess of Wales appealed for her family to have time, space and privacy when she announced her diagnosis for an undisclosed form of cancer on March 22, and said she had begun chemotherapy.

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’.”

As heir to the throne, William is Duke of Cornwall and 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.

He travelled to Hugh Town to break the earth for the new facility, which will provide care and inpatient beds and a maternity suite, and tour St Mary’s harbour, which is run by the duchy and handles everything from “Tripper Boats” to fishing vessels and cargo ships, making it a crucial part of island life.

When the duke first arrived in brilliant summer sunshine, he enjoyed the Isles of Scilly like any other tourist – ordering five pasties but joked they were not all for him.

He also revealed he donned a wetsuit on Thursday to go swimming in the waters around Tresco island – where it is rumoured he has spends breaks with his family.

William made a beeline for On The Quay cafe where staff had baked a bigger batch of pasties, with flavours from chicken and chorizo to Bombay potato, in anticipation of the future king popping in.

Asked by staff Joely Dearman, 22, and Zachariah Fox, 28, what type of pasty he wanted, the prince replied traditional and asked for five.

As everyone in the cafe laughed, he quickly added “they’re not all for me,” and said “it does smell delicious in here”.

He went on to tell them: “I was saying to the others, I can’t believe the islands today when you’ve got weather like this it’s just beautiful.

“I got in the sea yesterday which was good – I wore a wetsuit.”

After leaving the cafe, William chatted to tourists waiting for boats to take them to various islands, telling them “I said to the team, do we have to leave today? Can’t we stay a little bit longer?”

When one woman replied, “you can do whatever you want” he threw up his hands and said: “I wish, my family are very upset I’m here without them, my children will kill me if I don’t get back.”