King Charles’s cancer was caught early, Rishi Sunak has said as he wished him a full recovery.

The king, 75, is facing regular treatment for cancer after receiving a shock diagnosis during a recent hospital stay for a procedure on an enlarged prostate.

He has postponed all his public duties and begun medical care in London as an outpatient under the supervision of his specialist team of doctors.

Sunak said he was left “shocked and sad” when he was told about the diagnosis. The prime minister told BBC Radio 5 Live: “All our thoughts are with him and his family. Thankfully, this has been caught early.”

He said he hoped King Charles “gets the treatment that he needs and makes a full recovery … I’m of course in regular contact with him and will continue to communicate with him as normal.”

Asked what it meant for the day-to-day running of the country, Sunak said: “We’ll crack on with everything. He’ll just be in our thoughts and our prayers, many families around the country listening to this will have been touched by the same thing and they know what it means to everyone. So we’ll just be willing him on and hopefully we get through this as quickly as possible.”

Buckingham Palace announced that the king, who acceded to the throne 17 months ago, had a “form of cancer” on Monday. The royal family has asked for privacy but said he did not have prostate cancer after receiving diagnosis for a “separate issue of concern” while being treated for a benign prostate condition.

The Duke of Sussex has cleared his diary to fly to the UK to be with his father despite their troubled relationship, raising concerns about the seriousness of the king’s health.

The Prince of Wales’s return to official duties this week, after the Princess of Wales’s abdominal surgery, was announced just hours before news of the king’s diagnosis, suggesting William is stepping up while his father is unwell. Counsellors of state, who are appointed when a monarch cannot fulfil their duties as head of state, are not expected to be needed.

The king will still be dealing with his red boxes of state business and official papers, and holding privy council meetings, which can take place via video, and weekly audiences with the prime minister, which can be done over the phone.

Queen Elizabeth’s former press secretary Charles Anson told BBC Breakfast that the king felt “very strongly that the condition he has and the treatment for it should be known in general terms” out of a sense of public duty, but that people should not expect “daily bulletins”. The openness about the diagnosis was a “sign of the times”, he said.

He added that “the business of the country and the constitutional role of the monarch continues without really missing a beat”, with other family members able to step in when needed.

Charles personally called Harry and William, as well as his siblings, the Princess Royal, the Duke of York and the Duke of Edinburgh, to give them the news before it was publicly announced.

The palace said the king wanted to make his diagnosis public because of his long-running support for cancer charities.

The chief executive of Maggie’s, Dame Laura Lee, told BBC Breakfast that as president of the cancer charity, Queen Camilla was “very knowledgable about the impact of cancer”. She understands that cancer is “a very specific experience for each individual”, but that it also affects family members, who go through a “process of adjustment” after the shock of the news, Lee said.

“The king has done a wonderful job of telling us about his cancer diagnosis, he’s telling others that he’s going through this, they’re not alone, he is with them on that, but he’s also giving his time to his family to come to terms with what’s going on and to see what might lie ahead,” she said.

Lee added that people should take note of the king’s experience: “If you have a symptom please go to your GP, ask to speak to someone and look for those investigations which might uncover what an underlying problem can be. If they need to find someone to find that support how to navigate the system to get the care you need.”