As the King and his eldest son, Prince William, return to public-facing duties, speculation is mounting the royal family, including the Princess of Wales, will reunite for one of the most important ceremonial events on the British calendar.

Trooping the Colour, the King’s annual official birthday parade that is watched by the royal family from the Buckingham Palace balcony, could be just the day.

A smiling and healthy-looking King, 75, returned to work this week after being diagnosed in February with cancer, paying a visit to a treatment centre for the disease in London.

William, 41, travelled to north-east England, where he met finalists of his Earthshot Prize award in Durham, and also to Newcastle, where he opened a men’s charity, James’ Place.

Kate has been out of the public eye since the royal family’s traditional Christmas Day church service at Sandringham.

First she had major abdominal surgery in January, and then – in a video that sent shockwaves around the world – revealed she was being treated for an unspecified cancer.

Royal expert Gareth Russell told Us Weekly that it is possible she may be well enough to attend Trooping the Colour on June 15. He said it would delight royal fans “[but] … that could change at a moment’s notice”.

“The nation is gunning for Kate to get better,” royal expert Tessa Dunlop added.

“The monarchy needs her.”

Prince William has returned to work, but Kate still remains unseen. Photo: AAP

This isn’t the first time Kate’s possible attendance with William, and children George, 10, Charlotte (who turns nine on Thursday), and Louis, six, has been reported.

Before the princess spoke candidly about her cancer diagnosis in the March video, Britain’s Ministry of Defence jumped the gun and reported she was scheduled to be present at the review of the Trooping the Colour on June 8.

Kensington Palace wasn’t consulted about her appearance and Kate’s name was hastily removed from the official website.

“The princess will return to official duties when she is cleared to do so by her medical team. She is in good spirits and is focused on making a full recovery,” a Kensington Palace spokesperson said after her March 22 statement.

There has been no further update on Kate’s health and no date for her return, except a hint from William this week.

“Do you mind if I ask how your wife and children are?” a fan in Durham asked him.

“All doing well, thank you. Yes, we’re doing well,” the prince replied.

Although his diary will be carefully managed to minimise any risks to his health, the palace said the King might attend “some annual events”. These could include Trooping the Colour, as well as commemorations to mark the 80th anniversary of the World War II D-Day landings, also in June.

The Sun reported the King wants to ride his favourite horse, Noble, this year. Last year, he became the first monarch in 37 years to arrive at the ceremony on horseback (the late queen last rode in the parade in 1986 at age 60).

The King and Queen will also host a state visit by the Japanese Emperor Naruhito and his wife Empress Masako in late June.

The King’s health issues began in January when it was revealed he would be admitted to hospital to have a corrective procedure for a benign enlarged prostate.

The following month, the palace said tests had uncovered a “form of cancer”. No further details were given, beyond saying it did not involve his prostate.

The monarch has rested and been treated for the disease since then, continuing with official state duties in private. He was well enough to greet well-wishers after an Easter church service at the end of March.

The King’s illness came less than 18 months after he succeeded his mother Queen Elizabeth.

With his health improving, the King has ordered aides to “supercharge” his diary as he is “raring to go” after treatment, The Sun reported. He wants to be seen to “lead from the front”.