Princess Kate's first meeting with sister-in-law casts doubt on royal rift with Meghan Markle

However, an intriguing snippet from a new memoir by Kate's brother James, about his sister meeting his now wife, Alizee Thevenet, for the first time, paints a very different picture of the Princess of Wales.

He described how Thevenet appeared in the kitchen of the Middleton family home with her hair tousled and wearing nothing but his shirt, only to find Kate, William and their three children there.

Far from it being an issue, there was "no awkwardness at all" and by the end of the weekend Kate had given Thevenet her seal of approval, telling James the French financier was "just great".

This has now cast doubt on Meghan's claims that the Prince and Princess of Wales were "too formal".

Describing Kate's first meeting with Thevenet, James said his wife met his family by accident when the couple decided to stay at his parents' home in Bucklebury, Berkshire after attending a wedding nearby.

The next morning, he woke up to discover they unexpectedly had company - William, Kate and their three children were visiting for the weekend.

"I'm about to take a cup up to Alizee when she appears at the kitchen door," he recalled.

"She has just got out of bed, her hair still tousled, and she is wearing one of my shirts.

"In situations like this, Alizee is ­wonderfully French. She does not panic or rush upstairs to get dressed.

"Instead, she just greets everyone warmly as if it's not remotely unusual to be meeting her boyfriend's sister and brother-in-law for the first time wearing only an oversized man's shirt.

"'Hello,' she says, proffering her hand and with no awkwardness at all we're soon all chatting and the children are asking all kinds of cheeky questions at 100 miles per hour. Then we are all talking and laughing as if she has been part of the family for years."

He added that the next day when they parted ways, he got a "special squeeze" from his sister, who whispered in his ear: "She's just great."

By contrast, Meghan said there was some awkwardness with Kate straight away when they first met in 2017 and put it down to their very different styles.

Meghan recounted in the couple's Netflix series Harry & Meghan that she was "barefoot" and wearing ripped jeans when she first met Kate.

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Discussing the meeting, she said she did not know the "formality" the royals display in public continues behind closed doors and that she is a "hugger" – which she did not realise was "jarring for some Brits".

She said: "Even when Will and Kate came over and I was meeting her for the first time I remember I was in ripped jeans, I was barefoot. Like I was a hugger, I have always been a hugger I didn't realise that is really jarring for a lot of Brits.

"I started to understand that the formality on the outside carried through on the inside, that there is a forward-facing way of being and then you close the door and think 'OK we can relax now'.

"But that formality carries over on both sides and that was surprising to me."