Prince William grateful for public's messages of support
The Prince of Wales has expressed his gratitude for "the kind messages of support for Catherine and for my father, especially in recent days".
These were the first public comments from Prince William since the cancer diagnosis for his father, King Charles.
"It means a great deal to us all," said the prince, at a charity fundraiser for London's Air Ambulance.
Hollywood star Tom Cruise was also a guest, with the prince asking him not to "borrow" any of the helicopters.
With some irony, Prince William joked about the nature of the event for this return to official duties, after news about the Royal Family had been dominated by his father's illness and his wife Catherine's recovery from abdominal surgery.
"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!" said the prince.
But he gave no further details of how either the King or Catherine were progressing.
As a former air ambulance pilot himself, Prince William spoke of the need for new helicopters to support this emergency service and the "truly life-saving difference it can make", with the charity running an appeal to raise £15m.
He name-checked Tom Cruise as a surprise guest at the charity gala, held at a hotel in Westminster, but the prince hoped it wouldn't be bad news for the helicopters used for such medical emergencies.
"If you wouldn't mind not borrowing either of the new helicopters for the next Mission Impossible, it would be appreciated," said Prince William.
"We have all seen on our screens that, how can I put it, you seem to have a different take on normal wear and tear to the rest of us," he said.
King Charles's cancer diagnosis
Earlier in the day, the Prince of Wales had carried out an investiture ceremony at Windsor Castle.
Among those honoured were John Broadfoot, founder of SOS Kit Aid, whose charity sends second-hand sports kit to disadvantaged people around the world.
The prince was also pictured chatting with Ellen Convery, formerly known as Ellen White, who played over 100 games for the England women's football team.
Prince William's return to public duties follows a three-week absence which began after Catherine, the Princess of Wales, underwent surgery.
According to palace sources, Prince William has been focusing on being at the side of his wife and children, but he was now carrying out public engagements.
The King will continue to perform his formal constitutional role as head of state, but he will be stepping back from public events while he has treatment, with the type of cancer not being revealed.
With a sense of business as usual, an official message from the King has been published on Wednesday on the Royal Family's website, the first since the announcement of his cancer.
It's a formal greeting to Grenada on their 50th anniversary of independence, which makes no reference to the King's health.
The regular audiences between the King and the prime minister will continue to be in person, with the next scheduled in two weeks' time. Before that there was a "brief personal call" between Rishi Sunak and the King on the phone on Wednesday.
The King went to Sandringham in Norfolk on Tuesday, after a brief meeting with his son Prince Harry, who had travelled from California to see him.
The King's drive to Buckingham Palace, to get a helicopter to Sandringham, was the first time he had been seen in public since his diagnosis was announced.
There were reports the meeting between Prince Harry and the King lasted less than an hour and after one night in London, Prince Harry was seen at Heathrow airport on Wednesday, presumed to be returning to the United States.
There was no sign of a reconciliatory thaw in the relationship between Prince Harry and Prince William, after the tensions detailed in Prince Harry's memoir Spare.
As Prince Harry had arrived in London, sources indicated there was no plan for a meeting between the brothers.