LIZ JONES: How the past few days have shown us the depth of Kate and Charles's special relationship

It is the ultimate 'special relationship' since Kate became part of the Royal Family - exactly 13 years ago on Monday.

We've seen a comforting glance here and there, the warm smiles and fond greetings, a namecheck and a wink in formal speeches.

But this week, the huge esteem in which King Charles holds his daughter-in-law - the one who lives on this side of the Atlantic - was given a very public seal of approval.

On Tuesday, Charles admitted Kate to the Order of the Companions of Honour, making history in the process.

The Princess of Wales is the first member of the Royal Family to belong to this select group since the organisation was founded by King George V in 1917.

Kate and Charles embrace at the No Time To Die premiere at the Royal Albert Hall in London, in 2021

The pair found themselves together at the same hospital, the London Clinic in Marylebone, with reports suggesting that the King had 'toddled' from his ward to Kate's to make sure she was OK

She is in good company. The 65 members, drawn from the arts, science and medicine, include JK Rowling, Dame Maggie Smith, Sir Paul McCartney, Sir David Attenborough and Elton John.

Wow!

A keen amateur photographer in her own right, Kate is patron of the Royal Photographic Society, the National Portrait Gallery and the Victoria and Albert Museum.

But this honour is a reward for something more than her endeavours in the arts – it's about the high regard in which the King holds our future queen.

We saw a hint of the tenderness between them during last autumn's state visit to Kenya, when Charles referred to Kate as his 'beloved daughter-in-law'.

Camilla, Charles, William and Kate smile in their finery at the reception for members of the Diplomatic Corps at Buckingham Palace in 2023

A keen amateur photographer in her own right, Kate is patron of the Royal Photographic Society, the National Portrait Gallery and the Victoria and Albert Museum

This year came the shock discovery that both the King and the Princess must undergo treatment for cancer.

Partners in adversity, they found themselves at the same hospital, the London Clinic in Marylebone, with reports suggesting that the King had 'toddled' in his dressing gown from his room to hers to make sure she was 'OK'.

No surprise then that it's said they've become closer than ever.

The King invited Kate to lunch at Windsor last month, the day after she'd recorded the moving video message to the nation revealing her cancer diagnosis.

Charles told his daughter-in-law that he was 'proud' of her courage, according to The Times.

Such an intimate, reassuring moment would surely have helped her cope with her understandable trepidation about the following day's broadcast.

I imagine the Waleses' homes are full to the brim with cards and flowers right now from well-wishers, so the King must have been wracking his brain to come up with a different sort of gesture.

The King invited Kate to lunch at Windsor last month, the day after she'd recorded the moving video message to the nation revealing her cancer diagnosis

This honour is a clever and intuitive choice.

It's something that will inspire Kate for the future and the work she can do in an area that is important to her - supporting budding photographers everywhere, in war zones, in fashion, in news.

And it shows us, too, what a gift she has already, and in spades: the love and support of a generous, understanding father-in-law.

What could be better than that close but non-judgmental, no-pressure friendship as Kate recovers from the past few months of illness and stress?

Of course, she has a father and a brother as well as a loving husband in William. But these three men are, in a way, too close.

A born carer, Kate will have tried to shield them from her darkest fears in recent months, wanting to protect them.

Kate and Charles have an easy, humorous rapport. They will have shared their fears, their experience in hospital, but both are outward looking

With Charles it's different. He isn't detached, but he can certainly be pragmatic. He is also someone who is going through the experience of cancer, too.

There's an easy, humorous rapport, which helps. Yes, they will have shared their fears, their experience in hospital, but both are outward looking.

Let's not forget that the King is a fount of wisdom on all things 'Prince of Wales', offering insight on how to soothe and reassure, giddy-up and help wind her husband down.

Kate, in turn, is something of a conduit between two men who can both be stubborn.

The whole family should be grateful for her steely stoicism over Megxit – and her clever diplomacy.

It's said that Kate even played a part in ensuring that 'Recollections may vary' - a nugget of brilliance – was included in the Queen's response to Meghan's Oprah interview.

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Charles can rest assured that, as Queen, his daughter-in-law will handle any future conflicts with aplomb.

And underpinning all this is Kate's immense respect for the man she calls Grandpa, the man she is reported to save her deepest curtsies for.

Perhaps she is the daughter he wishes he'd had.

Kate has never been a prickly princess. She's without hard edges or resentment, so easy to be around. That easy, touchy-feely manner with her children seems to have rubbed off, making Charles soft and tactile with his grandchildren.

It makes me wonder if he wishes he were closer to Harry and Meghan's children, thousands of miles away in California.

A cancer diagnosis certainly puts squabbling into perspective.

And so does the love and regard between King Charles and his daughter-in-law that we have seen acknowledged in the past few days.

I imagine Kate is beaming from ear to ear, keen to get back to work, get stuck in, and repay the honour.

What a boost!