In every dark dynasty there is a figure who we pin our hopes on being the insurgent behind enemy lines. For a while we all believed Ivanka would be the voice of reason within the White House, and then there were the calls to free Melania from the prison of her marriage, neither of which have proved particularly on the money.

The fourth season of The Crown is not a pretty picture for much of the royal family, painting Prince Philip as a sexist bore, Prince Charles as a spoilt child, Prince Andrew as a creep in the making and The Queen as so unfeeling she can't give a hug to her daughter-in-law, while being overjoyed at the prospect of petting a horse.

preview for The Crown – Official Season 4 Trailer (Netflix)

So far there has been little time dedicated to the Queen's only daughter Princess Anne, despite Erin Doherty excellently capturing the unfussy and sardonic attitude which Anne is known for. In the fourth season we saw Anne bemoaning her marriage, furious at being told to end an extra-martial affair and seething about the comparisons between her and Princess Diana. Much has been made of the historical accuracies of this season, with criticisms for the break-in of Michael Fagan, Thatcher's voice, and even Charles's fishing technique in a particularly catty letter to The Telegraph. While viewers have been more than happy to take The Crown's word on what went on behind closed doors between Prince Charles and Diana, but when it comes to the Princess Royal they won't hear a bad word.

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Ever since Princess Anne seemingly refused to greet Donald Trump to stern consternation from the Queen, she has been celebrated as a symbol of resistance inside the stuffy monarchy. The Crown has captured her straight-shooting sensibility and tendency to eye-roll at what is expected of her. As she once said, "When I appear in public people expect me to neigh, grind my teeth, paw the ground and swish my tail - none of which is easy."

Some of The Crown's most interesting figures are those who aren't going to rule, painting the lack of purpose and waste in Princess Margaret's life as a Shakespearean tragedy which cements the resentment between her and her sister. Princess Anne, too, is arguably more interesting than her brother because of having lived her life in service to an institution which keeps pushing her further from the centre of it.

Yet so far Anne doesn't seem to be a key figure in The Crown's focus, with the Princess not getting a standalone episode as Margaret and Philip repeatedly do, and many of her scenes set up to give us hints about other members of the royal family. The new Anne fandom on Twitter has not taken this slight lightly, with many outraged that she isn't getting the screen time she deserves.

One of the main complaints is the omission of the Princess's dramatic attempted kidnapping from the series. The story goes that Anne was returning to Buckingham Palace following a charity event when the driver of another car jumped out and starting shooting, injuring her bodyguard and a journalist who happened to be there. Upon being told to get out of the car, Anne famously replied "Not bloody likely!", a fairly gutsy response to someone holding a gun.

The soundbite might be well known, but when discussing the event with Michael Parkinson Anne was equally relaxed about the event, saying she, "thought it was silly to be too rude at that stage," adding that she eventually "lost her rag" when he split the back of her dress.

Anne's meme-worthy responses and unusual candour might have made her an internet sensation, but it says more about our collective appetite for a rebel within the ranks of the royal family than anything else. There is so little emotion or breaking of convention that seeing someone behave like a normal person is pathetically thrilling.

The Crown is more interested in the darkness within this strange family – "the nastiness and competitiveness and the love and insecurity" as creator Peter Morgan says – which doesn't quite square with a subplot of Princess Anne being a boss babe. Perhaps a spin-off? Just don't expect the Princess Royal to be spurred on by the praise she's receiving, as when asked about the social network, she responded, "I know what Twitter is but I wouldn't go anywhere near it if you paid me frankly."

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