A rather chilly relationship: It's a picture that spoke volumes about the frostiness between Kate and Fergie's girls. Here we reveal what lies behind it 

Without doubt, it is a situation that few women would want to find themselves in: being photographed anywhere near the naturally elegant, uber-slender Duchess of Cambridge.

Spare a thought, then, for Princesses Beatrice and Eugenie. This week at a Buckingham Palace garden party, the sisters were pictured trailing in the wake of Kate, who was a vision in a fitted cream Alexander McQueen coat.

The three women weren’t walking together, gossiping companionably, as you might imagine, say, Zara Phillips, Beatrice and Eugenie might have done. More than that, the Princesses were giving the Duchess what would appear to be some rather chilly looks.

This week at a Buckingham Palace garden party, Beatrice and Eugenie were pictured trailing in the wake of Kate, who was a vision in a fitted cream Alexander McQueen coat

For who could outshine the flawless Kate? After all, even the world’s most glamorous women — from A-list actress Nicole Kidman to First Lady Michelle Obama — have been left looking a little dull in the Duchess’s radiant presence.

Poor Beatrice and Eugenie, despite being dressed up to the nines in a £1,700 Burberry dress and a £300 Alice + Olivia printed skirt respectively, simply couldn’t compete. As a result, the atmosphere between the three young royal women looked decidedly cool. Some say that this froideur, on what was supposed to be an idyllic occasion, a celebration of the Queen’s 90th birthday, is not new.

Tensions are said to have begun to surface in the early years of Kate’s relationship with William — and are rooted in far more than mere sartorial competitiveness.

And apparently, the frosty feeling between the trio (pictured here with Prince William at the Trooping the Colour ceremony in 2013) has only been intensified by what some see as Kate’s preferential treatment by The Firm ahead of Beatrice and Eugenie

From Beatrice and Eugenie remaining close pals with the one woman by whom Kate has ever felt threatened — the stunning Isabella Branson, whom William is said to have propositioned during the couple’s brief split — to perceived slights against Kate’s sister Pippa by the Princesses, the relationship between the three women is not as easy as it could be.

And apparently, this frosty feeling has only been intensified by what some see as Kate’s preferential treatment by The Firm ahead of Beatrice and Eugenie.

Take this week’s garden party as an example. One guest told me: ‘As William and Kate were ushered by a flurry of flunkeys down a long line of excited people, who stopped and stared or rushed forward trying to think of something to say, Beatrice and Eugenie were just left to go walkabout on their own — which they did very sweetly and well, spending a long time talking to all the people in wheelchairs. There was no sense of rush with them.’

Princesses Eugenie (left) and Beatrice (right) came under fire for their questionable choices of outfits at William and Kate's wedding in 2011

But, the same guest added, as William and Kate were the obvious ‘big ticket, box-office draw in neon lights’, the contrast between guests’ interest in the Cambridge couple and the York Princesses was acute.

‘As there were three separate garden parties, it might have been kinder to let Beatrice and Eugenie be the young stars in their own right at one of the other two, rather than go around in the shadow of the Cambridges. Few egos are small enough to cope with this kind of thing.’

As one insider puts it: ‘Royalty is all about pecking order, often in a cruelly blunt sense, and it is Kate who has all the toys and the position.

Kate and the York princesses have not always seemed to be on bad terms - she is pictured talking earnestly to Beatrice at the Olympic Games in 2012

And the Duchess was pictured enthusiastically greeting Princess Eugenie with a kiss at a gala in New York in 2014 

‘Despite being the only young “blood Princesses” (in other words, born royal), Beatrice and Eugenie have been reduced to walk-on parts in Royal Family life.

‘It particularly hurt when Kate did solo engagements with the Queen during the Diamond Jubilee. They felt snubbed.

‘Their father sometimes takes up the cudgels on their behalf — for example, when they lost their paid-for royal protection officers. But while the Queen is too old to make a fuss or rock the boat, Charles remains determined to have a smaller task force, namely himself, his own offspring and their families.’

A royal task force that emphatically does not include Beatrice and Eugenie, it seems.

It is hard to imagine that at one time, William and Harry and Beatrice and Eugenie felt almost like equals. When the Princes were children, according to a source, ‘Diana would take the boys swimming at Fergie’s house every Sunday’ and ‘in 1996, they all went on holiday together to the South of France.

Beatrice warmly greets an elderly guest at the Forgotten Association Garden party - also attended by the Cambridges - earlier this week

‘They were so close, despite the age gap [there are six years between William and Beatrice]. It’s tragic, really.’

Then Diana, the link between the two sets of children, died. And Fergie succeeded in embarrassing the family over and over again — offering access to Prince Andrew for money in 2010, to give just one example.

Charles sought to distance himself from Fergie. ‘He cannot stand even the mention of her name,’ said the source.

As the girls remain commendably loyal to their mother, perhaps it was inevitable that some kind of rift would appear between the cousins — and, in turn, with Kate.

The Cambridges and the Yorks frequently appear together at royal events and are pictured here at an equestrian event at the 2012 Olympic Games

Beatrice, who by all accounts is dedicated to her grandmother, is said to have been particularly upset at being sidelined — so much so that before the royal wedding, according to one source, she ‘went to confront, in a charming fashion, William about her role [within the Royal Family].

‘This was when he was living at St James’s Palace. He kept her waiting for ages, then said it wasn’t his decision what she was included in — all very friendly, but it didn’t achieve anything.’

Cracks began to show when conflict emerged between the Princesses and the Middleton sisters.

Apparently, there was an incident in 2008 at a London fashion show for Issa, a favourite brand of the Royals and the Middletons. Organisers asked an already seated Beatrice and Eugenie to shuffle up in the front row to make room for Pippa Middleton. It is said they refused.

Depending on who you talk to, this was a case of the Princesses being regal and unfriendly or Pippa being unnecessarily pushy because she didn’t want to lose face by suffering the social death that is being made to sit in the second row.

Kate allegedly snubbed Beatrice at her roller disco in 2008, where the Duchess memorably fell flat on her back

‘Pathetic, maybe, but however you look at it, people remember these things. They deplete mutual goodwill, if there is any to begin with,’ said one society girl who was there.

There was more trouble in 2008, when Kate organised a charity roller disco (at which she memorably fell on her back on the dancefloor, clad in sequins and hotpants).

It is said that, somehow, Beatrice wasn’t initially invited to the bash. Then, when an invitation was apparently extended to her — but not by Kate, according to sources — the Princess wasn’t made aware of the Eighties dress code and arrived in an ordinary dress, while everyone else was in neon outfits.

Beatrice, it seems, blamed Kate. Some say there were tears.

Then came the stress of the royal wedding in 2011, when the Princesses were doubly humiliated.

First, Fergie was very publicly not invited. Regardless of their mother’s actions, Beatrice and Eugenie could certainly be forgiven for agreeing with those who thought it a little small-minded of William, who controlled the guest list, to so humiliate her.

Second, and perhaps even worse, Beatrice’s long-standing boyfriend, Dave Clark, was not invited to the wedding.

Why? ‘William has the Spencer paranoia gene,’ says one source. ‘Dave is a gregarious, chatty American and William is so private it hurts. He would accuse his dog of being indiscreet if it barked at someone else too often.’

Fascinatingly, a few weeks later, Clark was asked to Zara Phillips’s wedding to Mike Tindall, even though it was a much smaller affair. ‘He was very friendly to [William and Kate] to show he didn’t mind,’ says a source. The snub, however, could not be erased.

That Clark is so convivial is revealing because socially, as a royal intimate points out, the Princesses could not be more ‘tribally different’ from William and Kate.

‘Beatrice and Eugenie have a very glitzy, international, party-girl streak — particularly Beatrice. They like the deck of a superyacht, a chalet pool, a New York dance floor or a hot new restaurant in LA.

The York princesses are known for their love of travelling and parties, with Beatrice in particular facing criticism for her many holidays

‘William and Kate are more at home among the red trouser brigade of north Norfolk or in East Anglian fields in their wellies, as Kate’s recent country-themed Vogue cover showed. They have no interest in befriending celebrities.

‘You can’t imagine them ever having dinner with Hollywood actors such as Ashton Kutcher and Mila Kunis, as Beatrice and Dave do, or hanging out with the artist Tracey Emin, as Eugenie does. They want to be with their children or have dinner at home with friends they have grown up with.’

And where their social circles do overlap, it seems to make relations trickier still. ‘Beatrice and Eugenie remain great friends with Harry’s ex, Chelsy Davy, who was never Kate’s soulmate. They are just such different people.

‘Worse, Beatrice and Eugenie are extremely close to Cressida Bonas, another of Harry’s blonde exes, and her half-sister, Isabella Branson.’

And, as we remember, if the flawless Kate has anything resembling an Achilles’ heel, it’s Isabella. Formerly Isabella Anstruther-Gough-Calthorpe, she is the leggy blonde with whom Prince William was once said to have been smitten, even supposedly turning to her during his break from Kate.

Beatrice and Eugenie are also firm friends with Cressida Bonas, the ex-girlfriend of Prince Harry

Today, Isabella is happily married to Sam Branson, the son of Virgin tycoon Richard.

But while she was invited to the royal wedding, she has not become friends with Kate — which is unusual, as the Duchess makes it a habit to be friendly to any women with whom William has history, such as brunette ex Jecca Craig or socialite Davina Duckworth-Chad.

Despite what you might think, Beatrice and Eugenie are not particularly affected by comparisons between their style and the Duchess’s — though it’s true that when Kate came on the scene, like Zara and Sophie Wessex, they seemed to upgrade their wardrobes.

Indeed, when Beatrice made her most publicised sartorial mistake — at the royal wedding, with her Philip Treacy ‘pretzel’ hat — she reacted with humour, selling it on eBay and giving the fee to charity.

The York princesses are also known to be close to Isabella Branson, said to be the only woman the Duchess of Cambridge is jealous of

‘If anything, Beatrice and Eugenie love fashion, its experimental side, more than Kate, though she gets all the attention,’ says one acquaintance.

What hurts far more, says the source, are taunts about their perceived workshy nature.

‘It isn’t fair. Beatrice works for Sandbridge Capital, a finance house, in New York, but has always been keen on charity work. Eugenie, meanwhile, works for Hauser & Wirth, a London art gallery.

‘People criticise them for having lots of holidays, but who’d turn down all those opportunities?

‘And what did Kate ever do when she was single? Take a few pictures for her parents’ party-planning website and spend a brief stint in the jewellery department at Jigsaw.’

It must be said that any friction isn’t universal between the families. ‘Prince Harry is immune to it all and is particularly good friends with Eugenie,’ says one insider. Another tells me: ‘Eugenie would never do anything to hurt William — they always have a laugh together.’

A courtier says: ‘Beatrice, in particular, has tried to build bridges but without much joy. William can be insufferably grand and it’s understandable if this has rubbed off on Kate.

‘The Duchess of Cornwall has gone out of her way to be nice to them, as if making up for things.’

Another source says: ‘Charles, too, is fond of them. They are sweet, well-behaved girls.

‘But it is challenging to start off feeling very royal and end up less so. And you can’t overestimate how hard it is being the child of Prince Andrew and Fergie. Yet look how well they cope.’

One almost feels sorry for the Princesses, caught on a shifting ladder of royal importance and facing a new world with a newcomer who attracts all the attention. Surely, only a churl wouldn’t forgive them the occasional sulky look.