Buckingham Palace and Downing Street were keen to demonstrate that King Charles remains in close contact with the government on Wednesday, even as he recovers from his first session of cancer treatment.

No 10 took the unusual step of confirming that Rishi Sunak would be telephoning the king in the evening after an agreement with the palace to disclose the information.

The prime minister’s official spokesperson said: “We don’t in general and we are not going to get into the habit of commenting on the PM’s conversations with the king. But we have agreed with the palace in this specific instance to confirm that they will be speaking on the phone later.”

Initially it was speculated that the formal weekly audience between head of state and prime minister, normally held in person and part of the monarch’s core constitutional duties, would be conducted over the phone.

However, a palace source later clarified it would be a personal call for the prime minister to wish Charles well and a speedy recovery, rather than an audience.

No audience had been scheduled for the next fortnight, partly in keeping with the pattern set by the late Queen Elizabeth II for this time of year, and also to allow the king to recover from his benign prostate enlargement procedure.

It is expected that on 21 February formal in-person audiences will resume, subject to any overseas commitments the prime minister may have.

Late on Wednesday the king issued his first public statement since his cancer diagnosis, as he marked Grenada’s 50th anniversary of independence from Britain.

He said: “I can only say how sorry I am that I cannot be with you in person to mark this momentous milestone … My thoughts are with everyone across Grenada, Carriacou and Petit Martinique, and all those in the Grenadian diaspora – ’one people, one family’ – as you celebrate everything you have achieved and all that your future holds. My family join me in sending our heartfelt congratulations to you all.”

Charles, 75, is at his Sandringham estate in Norfolk, having received outpatient treatment in London on Monday. Since he is unable to undertake public-facing duties for the foreseeable future, Prince William, 41, the heir to the throne, becomes the leading member representing the monarchy in public.

William hosted an investiture ceremony on Wednesday before attending a fundraising gala dinner for London air ambulance in the evening.

Addressing guests at the dinner, he said: “I’d like to take this opportunity to say thank you, also, for the kind messages of support for Catherine and for my father, especially in recent days. It means a great deal to us all.

“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 was expected to take over some engagements as the king’s diary was hastily rearranged and as Catherine recovered at Adelaide Cottage in Windsor.

He had said when the princess was admitted for the planned surgery that he would take time off to support his family and return to work only once her care and recovery had settled. Catherine, 42, is not expected to resume official duties until after Easter.

The rift between William and his brother, the Duke of Sussex, was highlighted once more with Harry’s arrival in the UK on Tuesday to see their father.

Suggestions that the family crisis could lead to some form of reconciliation between the siblings, after Harry’s highly personal attacks on his family in TV interviews and his memoir Spare, would seem unfounded: sources close to William have said there were no plans for the two to meet while Harry was in the UK.

Charles was briefly reunited with Harry on Tuesday after the duke’s overnight flight from Los Angeles. They spent about 45 minutes together at the king and queen’s London residence, Clarence House, before the king and queen flew by helicopter to Sandringham.

It is not known where Harry stayed while in the UK. The Duchess of Sussex remained in LA with their two children, Prince Archie and Princess Lilibet.

Harry was seen at Heathrow on Wednesday on his way back to Los Angeles about 24 hours after he flew in to see his father.

William is understood to have made clear that his priority is to support his wife and children at their own difficult time, with no timescale being put on that. His role as Prince of Wales, which he inherited 17 months ago, has suddenly been thrown into sharp focus after Buckingham Palace’s announcement on Monday of the king’s diagnosis.

Sources have reportedly indicated that after Wednesday’s duties, William may not be seen again for some time. Buckingham Palace, meanwhile, will be liaising with Kensington Palace over which of the king’s engagements William might undertake on his father’s behalf.

The king has postponed all public-facing duties but is continuing with behind-the-scenes work on his red boxes of state papers.

He received his diagnosis while undergoing a procedure for benign prostate enlargement. Details of what form of cancer he has have not been made public, but Buckingham Palace has confirmed it is not prostate cancer.