There are two horror stories in The Birds, Alfred Hitchcock's movie about what happens when birds turn bad: the horror story you can see and the one you can't.

First: the one you can see. You might remember some of its worst moments. Like the scene where the old woman goes to look for the farmer and finds his body slumped against a wall, his eyes pecked out. Or the scene where Melanie Daniels, played by Tippi Hedren, goes into the attic and the birds strike. It's still shocking, that scene, and the worst of it is there's no music – just the sound of wings flapping. It's something normal transformed into something horrific. Alfred Hitchcock loved doing that.

Then there's the horror story you can't see: what happened to Tippi Hedren during the making of that 1963 film, the long-term effects the experience had on her, and the obsessive and destructive relationship she had with Hitchcock. As new BBC film The Girl makes clear, Hitchcock promised Hedren she would be perfectly safe in the attic scene and that only mechanical birds would be used. In fact, live gulls, ravens and crows were thrown at her – for five days. Was that terrible, frightened look on her face acted or real?

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The Girl, which stars Sienna Miller as Hedren, offers a fictionalised version of those days, but it's based on interviews with Hedren and what she really thought about Hitchcock. Asked to sum up the director in one word, she chose "evil". Asked what the worst thing he ever said to her was, she chose: "You will do whatever I want, whenever I choose." And asked about the long-term effects of their relationship, she said: "I was the recipient of his dark side. He became obsessed and when the demands became so impossible, I said 'I want to get out of my contract'. He said 'I'll ruin your career', and he did."

In researching her role as Hedren, Miller – who delivers a remarkably mature performance after years of paper-thin material like Alfie and GI Joe – went out to California to meet the actress. "It's a big responsibility when you're playing someone that existed, especially when they're still alive," she says. "I went to Los Angeles and met her and spent the day with her. She's been really helpful and has been on the end of the phone and we've been emailing."

What Miller says she saw in those films is what we all see in Hitchcock's work: tension and horror but also, in film after film, an obsession with women. In that sense, Tippi Hedren was nothing new because there were blonde women before her and there were blonde women after her; women who were slapped and strangled and raped and murdered – and idolised. Does this mean Hitchcock was a horrible person? Hedren says he was, and the scriptwriter says he was. Hitchcock is not here to deny it.

This imbalance shows through in the finished film: while the characterisation and portrayal of Hedren is convincing, the characterisation and portrayal of Hitchcock is much less so, probably because Toby Jones, who plays him, had to rely on YouTube clips as research whereas Miller met Hedren and clearly understood and sympathised with her.

"She was a strong, independent woman," says Miller. "She found Hitchcock endearing and hilarious. He could be charming and funny. In the 1960s she was an unknown person suddenly flung into this world of movie stars and glamour. Things were wonderful and she felt part of Hitch's family. Then gradually, as his obsession built, the relationship disintegrated."

All of this obsession and disintegration is in The Girl: how Hitchcock spotted Hedren in a television ad; how he took a model with no movie experience, screen-tested her and told her he would make her a star. In Miller, you can see the tension between the desire for this to happen and her increasing horror at Hitchcock's desires. The uncomfortable question is: how much would you put up with to become a film star?

"I think Tippi was uncomfortable with his advances and his way of being," says Miller. "He would often tell filthy limericks, which she didn't particularly appreciate, and there were several times when he made attempts to be romantic with her, which she brutally rebuffed.

"It was probably that stoicism and her ability to withstand his attentions that made him more obsessed with her. She dealt with a lot of difficult things, but she dealt with them with real grace and elegance."

Miller firmly believes the portrayals of Hitchcock and Hedren in The Girl are balanced and you leave the film with an understanding of both. But do you really? Jones's Hitchcock is much more cartoony than Miller's Hedren and this may be because Jones has to play the director under lashings of prosthetics and make-up.

This physical transformation was hard work for Jones and took three to four hours every day on set. First, there was the bald pate, then a prosthetic chin (which is not always convincing in the film), then false teeth to get Hitch's sticky-out bottom lip. Finally, there was a fat suit, and there it was: the famous rotundity of the only man in history who could turn sideways to create a brand. "The physical transformation was more extensive than anything I've experienced before," admits Jones.

The challenge of it all, he says, was to find the right balance between suggestion and imitation – a balance he doesn't always get right – and perhaps the trickiest part was the voice. Hitchcock had the most extraordinary way of talking: slow and ponderous, which is often how powerful people talk because no-one is ever going to interrupt them.

"I worked with a terrific voice coach and we explored Hitchcock's voice in two ways," says Jones. "The first is the physical, what is happening in his mouth, throat and how that resonates through his body.

"Then secondly, psychologically, speculating on how and why his voice evolved in that way. Then there's a lot of secondary research, reading and watching. Thankfully, Hitchcock was no shrinking violet so there's a lot of footage of him. The truth is, though, that much of this secondary research is just a way of staving off the panic of playing someone well-known."

By the end of the process, ambivalence is probably the best way to sum up Jones's feelings about Hitchcock. "He presented such a consistent and celebrated image to the world and yet his films, his childhood and his evident obsessions contradict the coherence of that image," he says.

"Hitchcock recognised certain qualities in Tippi he was used to working with. She was a blonde and had a certain sophistication, which was common to a lot of actresses he chose. And he became more and more intrigued with that part of her that he wasn't able to control."

This might have been one of the factors that led to Hitchcock offering Hedren the lead in Marnie, the film he made after The Birds. But by the time she had finished making Marnie, Hedren had had enough. She walked away and Hitchcock stuck to his word to ruin her: even though he never made another film with her, he kept her to her contract, meaning she couldn't make movies with anyone else.

The writer of The Girl, Gwyneth Hughes, says there were two victims of this act of spite: Hitchcock, who never got over the collapse of his personal and professional relationship with Hedren; and Hedren, the blonde icon who fell and never got up.

The great shame is that The Girl doesn't really get this across – it is much more about Hedren than Hitch – but the greater shame is that Hitchcock is not here to tell us what he thought, or maybe even make a film about it. Which is what he did in a way. Over and over again: films about beautiful women and obsession and men running away from guilt and responsibility and shame. It's in those great films – not The Girl –that we'll find the real story.

The Girl is on BBC Two at 9pm on Boxing Day.