One principle of hereditary monarchy is that it is the institution, not the individual, that prevails; the “Firm” over the figure on the throne.

Following King Charles’s cancer diagnosis, Buckingham Palace and the government can point to laws as evidence the well-oiled machinery of monarchy will continue to whirr efficiently in the background as the king retreats for treatment.

Dusty statutes, however, cannot legislate for the visceral reality that events this week have exposed not only the physical fragility of the king, but also the current state of the House of Windsor.

Charles, figurehead and focal point of the royal family, will be unseen, and for how long is not known. The Prince of Wales, as heir, will be expected to step up. But his wife is still recuperating from abdominal surgery, his children are young, and, aides have made very clear, they are absolutely his priority.

Joe Little, of Majesty Magazine, said: “It’s a difficult situation, particularly so early in the reign. The fact that the Prince of Wales is also more or less out of the equation at the moment does most definitely expose the fragility of the monarchy. And hopefully that’s something that will be addressed.”

Despite the “keep calm and carry on” message from the palace, the language does betray uncertainty. Aides speak of the king “hoping” to continue with select meetings in private, of it being “too early” to know when he will resume full public duties, and counsellors of state “not expected” to be necessary to stand in.

For Charles, it is the latest in a series of blows. “On a personal level it’s been incredibly tough for him with all the family situations going on. The loss of both parents, the loss, in a manner of speaking, of his younger son, will have been devastating to him.

“But it could well be that King Charles III is able to cope in the same way that his mother could cope, that she could compartmentalise these issues,” said Little.

Mechanisms through which the monarchy will steer itself during the unsettled period ahead, include, what the constitutional expert Prof Robert Hazell has termed “a soft regency”. Senior royals can perform many of the king’s functions without counsellors of state needing to being appointed, he said.

“There is only a very limited amount the monarch has to do constitutionally. Much of the rest can be done by others,” said Hazell, founder and director of the constitution unit at University College London, whose recent blogpost covers the constitutional impact of Charles’s diagnosis.

“I don’t think there are any serious gaps in the legal and constitutional framework. I think the main thing it exposes is not something that is constitutional, it’s the diminishing size of the royal team. I think for the palace that is potentially quite a serious problem.”

What the public care about, he said, is seeing the royals. “It’s the ceremonial side and the welfare side of the monarchy which matter to the public. Queen Elizabeth II famously said ‘to be seen is to be believed’. She fully understood that they needed to get out there,” added Hazell.

“The one time in our history when the monarchy has become seriously unpopular, and there really was quite a republican movement, was when Queen Victoria went into hiding after Prince Albert died. Quite level-headed politicians at the time thought there was a real risk of us becoming a republic.”

The shortage of working royals is a real dilemma for Charles. Since George V, the House of Windsor has seen its visibility as key to its survival: photo-ops at hospitals, schools, markets, military parades, the ceremonial pageantry – all crucial in the mix.

This is how the people have been served up monarchy for generations, and there had been no radical change to that recipe.

Now, with the departure of the Duke and Duchess of Sussex and Duke of York as working royals, the core pool comprises the king, queen, Prince and Princess of Wales, Duke and Duchess of Edinburgh and the Princess Royal – the youngest in their 40s, and the king and queen in their mid-70s. The Duke of Kent (88), Princess Alexandra of Kent (87) and Duke and Duchess of Gloucester, aged 79 and 77, continue to perform some duties.

Charles wanted a “slimmed down” monarchy, though reckoning without developments on the Harry and Andrew fronts. And it may have seemed an answer to critics baulking at the cost of the royal family. To now increase its size would surely increase those costs if it continued to operate in the way it has. In these days of austerity, that would risk attracting unwelcome headlines and scrutiny.

The result is that while Charles undergoes treatment, for however long, Prince William, 41, as heir will become a temporary figurehead and the most senior of the small number of visible royals. It is thrust on him just 17 months after inheriting the title, and at a time when , on top of his duties at home, the rift with his brother continues.

“The Prince of Wales lacks the training of his father, who was heir from the age of three,” said Little. “There’s nothing to indicate William is not going to cope with anything that is thrown at him. He has already represented his father, and his grandmother, abroad on occasion. He shows all signs of being a good statesman. But it is early on and his priorities lie with his ailing wife and their young family.”

We are a long way from regency. But should Charles become permanently incapacitated, William would be appointed regent.

As Prince of Wales and now king, Charles has always had the support of his siblings. At present, this is something William lacks.

And, although all constitutional bases may have been covered, there is one intriguing, albeit highly unlikely, scenario.

According to Hazell, in the unthinkable event of both the king and Prince of Wales both becoming permanently incapacitated at a time before William’s children were to reach the age of majority, step forward Prince Harry, as next in the line of succession.

To prevent that would require legislation, he said. A recent example was in 1953 when legislation was passed to allow Prince Philip to become regent instead of Princess Margaret while the late queen’s children were underage.

“That’s the law,” said Hazell. “Legally the Regency Acts are quite clear. And if for any reason either the palace or government didn’t want Harry to be regent, they would need to legislate.”