The Queen says the King is doing “extremely well under the circumstances” following his cancer diagnosis, in her first public update since his illness was revealed.

The Queen was asked about her husband’s health while on a charity visit to Salisbury on Thursday (British time).

She said her husband, who had his first round of cancer treatment earlier this week, was “very touched” by all the messages of support he has received from the public.

The 75-year-old King is staying at Sandringham following his diagnosis, which was announced by Buckingham Palace on Monday.

He hosted a whirlwind visit from his son the Duke of Sussex on Monday and the royal family have received many messages of support from the public during royal events in recent days.

The Queen left the monarch at Sandringham to fulfil her royal engagement at Salisbury Cathedral. Among the first people she met were medical staff from Wiltshire Air Ambulance.

“I do hope His Majesty is doing well … we’re all really sad to hear the news,” Ben Abbott, 40, a critical care paramedic, said.

The Queen replied: “Well, he’s doing extremely well under the circumstances. He’s very touched by all the letters and the messages the public have been sending from everywhere – that’s very cheering.”

The King has postponed all public-facing duties while he has his cancer treatment. He will continue with behind-the-scenes work on his red boxes of state papers.

Heir-to-the-throne Prince William may step in to represent his father at an event. But so far no engagements have been scheduled.

The Prince of Wales returned to public duties earlier this week, with an investiture at Windsor Castle and a fund-raising dinner for the London Air Ambulance charity in London.

He thanked well-wishers for their support during the twin medical crises the royal family is facing.

“It’s fair to say the past few weeks have had a rather medical focus, so I thought I’d come to an air ambulance function to get away from it all,” William said.

The Princess of Wales left hospital last Monday after major abdominal surgery that is expected to keep her sidelined until after Easter. She is recuperating at the couple’s home, Adelaide Cottage in Windsor, and has been reunited with her three children.

-with AAP