RICHARD KAY: The very telling reason why Harry and the Royal Family's relationship is more broken than ever

It is, of course, convenient to blame a busy schedule for ­everything. And on the face of it, the King was very busy yesterday.

From Windsor Castle where he had spent the Bank Holiday, he had an audience with Fiji's prime minister at Buckingham Palace, followed by a meeting with senior military commanders, and then medical appointments connected to his ongoing cancer treatment, the last of which are followed by an ­obligation to rest.

Today promises more of the same, including a Palace garden party and his regular weekly sit down with PM Rishi Sunak, who after last week's drubbing for the Tories in the local elections may need more consoling than usual.

What there most definitely was no time for amid all this coming and going, was any kind of get together with his younger son. Prince Harry's arrival in Britain had triggered speculation that father and son would meet. 

Some had even boldly suggested that such a meeting might, at long last, start a process of reconciliation between the King and Harry. Indeed, there was even murmur of an olive branch being extended.

Far from Harry's hope of reuniting with his father in the wake of the King's cancer diagnosis, the illness has, if anything, added to their estrangement

Instead, the hand-wringing excuses of 'full diaries' offers a different and, for Harry, a more ominous message. Unlike that dramatic flying visit in February, where the Prince was granted a less than 30-minute meeting just after Charles's cancer diagnosis had been made public, the palace gates remained firmly closed.

Pointedly, it was the Duke of Sussex's team that broke cover with a spokesman explaining that a meeting 'unfortunately will not be possible due to His Majesty's full programme'.

Even with the acknowledgement that Harry recognised his father's 'commitments and various other priorities', the nuance in the bulletin was clear: the failure to meet was not Harry's fault. So much for olive branches.

Prince Harry's arrival in Britain for The Invictus Games Foundation Conversation had triggered speculation that father and son would meet

What then is going on, and what do events tell us about the state of relations between the exiled Harry, his father and the rest of the Royal Family?

One conclusion would suggest that, far from his hope of reuniting with his father in the wake of the King's cancer diagnosis, the illness has, if anything, added to their estrangement.

But, in fact, I understand that there had been no formal request from either the King or his son to schedule a meeting. For Harry also had a packed programme. From his overnight flight from Los Angeles, he was whisked to an event for the Invictus Games, his project for wounded and former armed forces personnel, at Armoury House in East London.

Although little more then three miles from Buckingham Palace, he might as well have been on a different continent as far as meeting his family was concerned.

Charles met with Fijian PM Sitiveni Rabuka yesterday while Harry arrived in the UK

And today, while the King hosts the first garden party of the year, the Prince will mark the tenth anniversary of the games with a service at St Paul's cathedral. If Harry had been so set on seeing his father, it is tempting to wonder why he didn't fly over a day or two earlier when Charles had no official duties. How significant that might have been if they had been together on the first anniversary of the King's coronation. Inconveniently, that fell on Prince Archie's fifth birthday and Harry chose to spend it with his family in California.

Once, Harry's return visits to the UK meant it was relatively straightforward for him to drop in on his father, but he no longer has royal accommodation. And, intriguingly, he made no request to stay at any royal residence for this two-night visit.

This alone suggests that chances of a rapprochement are more remote than ever. Trust too has evaporated in the 16 months since Harry's explosive memoir Spare, with its excoriating attacks on Camilla, ­William and Kate.

Harry speaks onstage with Sir Keith Mills to mark ten years since the inaugural Invictus Games in London 2014

The two men once shared a special bond, but each meeting between them became distracted with the weight of ­previous disappointments.

Some old friends were surprised that given his Christian faith, a King who practises humility and empathy as a matter of course, could find no time to see his son. Others argued that no blame could surely be attached to Charles if he viewed such encounters with his son as more a burden than a pleasure.

What is certain is that notwithstanding that busy workload, two figures would have viewed the prospect of a meeting between the King and Harry deeply troubling — Queen Camilla, who was hurt by ­Harry's lacerating attacks, and Prince William who will not ­forgive his brother for his comments about Kate.

Last month, the historian Tessa Dunlop suggested Harry was in a 'painful place' following the Princess of Wales's cancer diagnosis and William's remarks.

'The opposition of Camilla and William would be formidable to Charles,' says a courtier. 'For all his affection for Harry — which remains — and sadness at the deep rift that has developed, his ties with his wife and older son are far deeper.'

Perhaps the most telling observation on the broken relationship between Harry and the royals came in, not off-the-record briefings yesterday, but publication of a future joint engagement between the King and his son — the other one.

Next Monday, Charles will, amid a colourful ceremony, formally hand over the role of Colonel-in-Chief of the Army Air Corps to Prince William.

Harry, of course, enjoyed a distinguished career with the combat aviation arm of the Army, serving with considerable bravery as a helicopter pilot in Afghanistan. This passing of the baton, however, speaks more eloquently of a united family. Increasingly, it is hard to see Harry ever again fitting in.