Buckingham Palace announced on Monday that Charles, 75, on the throne for less than 18 months since the death of his mother Queen Elizabeth, had been diagnosed with the disease and would postpone his public engagements to undergo treatment.
Charles waved to passers-by on Tuesday afternoon as he was driven the short distance from his Clarence House home in central London to Buckingham Palace. He and his wife Queen Camilla then took a helicopter to his Sandringham estate in rural eastern England to begin his recuperation.
Shortly before the king's departure, Harry, who has fallen out with the rest of the royal family since he stepped down from royal duties almost four years ago, was pictured arriving at Clarence House, and had a brief reunion with his father according to newspaper reports.
However, a royal source said there were no plans for Harry to see his elder brother, heir-to-the-throne Prince William, during his visit to Britain.
William is expected to step up to fulfil some of the monarch's duties, along with other senior royals while Charles begins a series of out-patient treatments.
Despite the diagnosis, Charles is planning to continue with much of his private work as monarch including his weekly audience with the prime minister and dealing with state papers. Sunak said he was in regular contact with the king.
"That will of course continue as normal and we'll crack on with everything," he said.
The cancer was discovered when Charles stayed three nights in hospital last month where he underwent a corrective procedure for a benign enlarged prostate. Beyond confirming it was not prostate cancer, the palace has not given any further details.
The royal family usually keep medical matters private, but the palace said Charles had chosen to go public as he was patron of a number of cancer-related charities.
While the king will receive expert private care, his diagnosis will draw attention to Britain's rising cancer waiting times within the state-run National Health Service (NHS) which is widely regarded as being in crisis.
Survival rates for cancer in Britain lag those of other European countries for nine out of 10 of the most common types of the disease, according to an NHS Confederation report published in January.
The surprise diagnosis, which has dominated British media since the announcement was made, is another personal blow for Charles during his year and a half on the throne.
Early last year, Harry published his autobiography "Spare", which contained damning revelations about his father and elder brother, while Charles has also had to contend with ongoing allegations against his brother Prince Andrew relating to the late sex offender Jeffrey Epstein.
Harry, who quit royal duties in 2020, jetted back to Britain from California where he lives with his American wife Meghan and two children to see his father after Charles told him and his other immediate family of his diagnosis.
The king's cancer revelation comes as Kate, the Princess of Wales and wife of heir William, recuperates at home after spending two weeks in hospital following planned abdominal surgery for an unspecified but non-cancerous condition.
She is not expected to return to public duties until after Easter and the absence of the senior figures will put pressure on the other working royals to perform extra engagements.
Charles has always been keen to have a more slimmed down monarchy but with his younger brother Andrew and Harry no longer involved, all those who currently carry out royal engagements are aged over 50 apart from William and Kate, with some now in their 80s.
His sister, Princess Anne, often tops the list for being the busiest royal, followed by Charles.
Royal biographer Matthew Dennison said that Charles, as a workaholic, would be impatient to return to "the everyday business of the public side of monarchy."
