On this, at least, everybody can identify with King Charles. His cancer diagnosis this week is a traumatic moment, and not just for him but for his family. It has also triggered instinctive public sympathy, not least for the monarch’s refreshing relative openness about his condition. All this has fired up a powerful media story, made more irresistible by the Prince Harry subplot, that will be part of our national life for months.

But do this week’s events actually have institutional implications for the monarchy? The instant reflex of many will be to say no. The British monarchy’s recent history of adaptiveness, under Queen Elizabeth II and now Charles, points that way too. After all, “the firm” is hardwired for continuity. Seamless adaptation is what the monarchy does. It has been doing it again this week, albeit wrapped in the privileged language in which going back to work becomes the “resumption of duties”. Few politicians have any interest in questioning any aspect of this.

Yet the king’s diagnosis is still a shared national shock. It reverberates more widely than if the sufferer were you or me. It was also very unexpected. Coming so soon after the end of Elizabeth II’s unprecedentedly long reign, it poses governance questions that are unfamiliar to rulers and ruled alike. The country is not used to being presided over by a withdrawn or sick sovereign. This has set people thinking and talking. It is silly to pretend otherwise, and sillier still to disapprove of discussing it.

Looking back, this thinking and talking did not happen enough when Elizabeth II died. She had been there for so long that the transition to Charles occurred in a kind of collective disbelieving daze that the fateful moment had finally arrived. As a result, the national conversation in September 2022 tended mainly to look back to the past, not forward to the future. The new king was already a deeply familiar figure. This ensured as stable and unquestioning a transition as is possible to imagine.

This week’s intimation of royal mortality feels suddenly different. It asks us to take on board properly, in a way that remained secondary in 2022, that this royal reign will be significantly shorter than the last. It whispers insistently to us that one day – still perhaps years off, but perhaps instead disconcertingly soon – both the monarchy and its relationship with the nation will have to evolve again.

This is a bigger question than some would like to believe. Nor should it be ducked. Doubters should instead look at two opinion polls conducted in January. Each reveals a British public whose belief in the monarchy is far more lukewarm and nuanced than you might imagine from watching the news bulletins this week or from reading the papers. They remind us, in particular, that Britain needs to reckon with generational changes, both in public attitudes to the crown and among those who wear it.

The polls, by Savanta and YouGov, have produced strikingly similar headline findings. In Savanta’s poll, 48% of adults say they would prefer Britain to have a monarchy, against 32% who prefer an elected head of state, with 20% saying they don’t know. YouGov’s figures, in answer to a similarly worded question, are 45% for monarchy, 31% for an elected head of state and 24% who don’t know. Older voters are more emphatically monarchist in both polls. Among younger voters, however, there was a clear preference for replacing the monarchy with an elected head of state.

None of this should be taken to imply that Britons, even the younger ones, are bursting with republican enthusiasm. They are not. Other polling questions on monarchy also show less stark divides. But two polls in recent weeks both showing that, for the first time ever according to the Republic campaign group, the monarchy lacks the overall majority support of the population should make politicians, as well as courtiers, think. So, in particular, should the confirmation in both the polls that younger adult Britons are far less committed to the monarchy than their parents or grandparents were. And this generation gap seems to be widening.

There are also striking differences between particular parts of Britain. In the YouGov poll, there are more people in support of an elected head of state, as opposed to a monarchy, in Northern Ireland, Scotland and London. This is a reminder, nevertheless, that the monarchy is one of the relatively few British institutions that actively promotes a UK-wide sense of identity. King Charles seems to be notably well aware of this. Unionism comes very naturally to him. But how far is that true of his son Prince William, who grew up during the years when the bonds of the UK were weakening?

In his new book Fractured Union, Prof Michael Kenny of Cambridge University analyses three contrasting constitutional paths facing the UK: break-up, overarching reform and gradual evolution. Of these, he argues, the third is the most likely. But it is not the easy option. As Kenny stresses, the pragmatic evolutionary path also requires the constant management of a national dissensus, not a national consensus. It requires enormous care and sensitivity. Modern British politics has not been very good at that, to put it mildly.

The king’s cancer is a reminder that a similar choice between abolition, reform and evolution inevitably faces the monarchy. Britons are divided, not united. The public appetite for opening up these questions and examining them may be low, especially when compared with other, more pressing problems. But even if the king returns to relative health, the issues will not go away.