Sarah Wines: One gets the impression William and Kate would prefer to avoid Harry and Meghan

As various working members of the royal family were spread across the country yesterday – the Duke and Duchess of Cambridge in Wales, princess anne Epsom, Earl and I Countess of Wessex in Belfast – Duke and Duchess of Sussex Celebrating the first birthday of his daughter Lilibet in Windsor.

Maybe they have come to the palace to meet the queen? One can imagine that Her Majesty – who had never met her great-granddaughter until last week – would have been delighted.

Under normal circumstances this might have been turned into a big occasion, a chance for many generations of the family to come together and make some memories, as they have recently put it themselves.

After all, the Queen isn’t the only relative Lilibet — or, for that matter, her older brother Archie — has had little chance of getting to know.

Uncles, aunts, cousins, their grandfather Prince Charles – all remain virtual strangers to Sussex children. Which is a shame because, as Prince Harry knows from his close friendships with his own cousins, Princesses Beatrice and Eugenie, family ties matter.

Prince William and Kate, Duchess of Cambridge, pictured leaving Thanksgiving service at St Paul’s Cathedral yesterday

There is a shared experience that can be invaluable, especially when things get tough. It feels sad to deprive the little Sussexes of this.

But this was not to happen, anyway, not on this occasion. Although we don’t know for sure, it looks like Prince George and Charlotte didn’t attend Lillibet’s birthday as they were in Cardiff with their parents.

As far as William and Kate are concerned, one seems to have a clear impression that they would rather attend an envelope opening on Mars than Harry and Meghan face-to-face.

The same impression was certainly given at St. Paul’s Cathedral on Friday, where there was not a single glance between the two couples.

Fair enough, they were on opposite sides of the cathedral and arrived separately. But you would never have known that brothers were relatives too, once they ended each other’s sentences far away from the point of being so close.

The stone-faced Prince Harry pictured at the service of Thanksgiving at St. Paul's Cathedral on Friday

The stone-faced Prince Harry pictured at the service of Thanksgiving at St. Paul’s Cathedral on Friday

The only thing they seemed to have in common was their rocky facial expressions.

If ever there was a time to bury a hat-trick, it was this celebration of the Queen’s very special birth anniversary. After all, no one understands better than Her Majesty that sometimes there is a need to set aside one’s feelings for the greater good.

It would have been a big and meaningful gesture, a real tribute to his sacrifice. And yet even for that they could not manage it. To be honest, I felt like beating the thick skulls of both of them together.

That said, I still had a vague hope that it was protocol, not pride, to keep them apart at St. After all, this was a highly formal setting, and few things are much easier in a more relaxed environment.

Last night’s Buckingham Palace concert, in the presence of rock royalty, may be the perfect opportunity to clean the air more casually. A hug, a shared song, a little bop – everything sounds less serious when you’re having fun. But no. Not even that. Harry and Meghan were reportedly hiding at Frogmore Cottage (the current cost of living somewhere north of a week at The Ritz).

One might say the only reason the Sussexes showed up was to get the all-important snap of Lillibet with Lillibet and recharge their Royal status for Netflix.

Equally though, it is clear that Prince William is in no mood to compromise. Maybe he knows something we don’t. Eventually, the much-loved tell-all memoir by Harry was scheduled for publication this autumn. It’s hard to imagine any revelation more damaging than any of the revelations in the Oprah interview, but you never know.

And why are the Cambridges always the ones offering the olive branch, especially when they only end up with prickly eyes with it?

Either way, one thing is clear. Even the queen herself, with her remarkable ability to bring people from all different backgrounds together, cannot bridge the gap between these two brothers. A sad footnote to an otherwise happy weekend.