IN AN anonymous Berlin hotel room, Rosamund Pike is resting her feet on the chair in front of her, her knees drawn up to her chin. Wearing black jeans, a lacy blouse and grey nail polish, she looks pensive, made more so by a thick light-brown fringe she has styled down her forehead. Is it for a new role? “The hair?” she says, surprised. “I think that’s much more about hiding! A bit of reclaiming of something of myself. This is just me having a change.” She probably needs it.

We meet with Pike in between characters. She’s just finished A Private War, in which she plays real-life Sunday Times war correspondent Marie Colvin, who lost an eye from a Sri Lankan army RPG and was later killed in Syria. “She’s a woman who I have to do justice to on film,” Pike says, earnestly. “She lived with an intensity that was a very beautiful and troubling thing.” In a couple of days, she’s off to Budapest to play “an astonishing woman”, pioneering scientist Marie Curie, for the film Radioactive.

It’s symptomatic of the position Pike is now in. Now 39, an age when many actresses struggle to find roles, this British star is finding increasingly complex characters. “One keeps, you hope, getting better,” she says. “You have to get opportunity and if you want to change things, you have to seek out what you want to do and you have to say ‘no’ to the things that come easily. That’s the thing. You say ‘no’ to the things that come easily and you fight for the things you want to do.”

Amongst the things worth fighting for was her latest film, Entebbe. She plays Brigitte Kuhlmann, one of four terrorists who famously hijacked an Air France plane en route from Tel Aviv to Paris in 1976. Diverting the aircraft to Entebbe airport in Uganda, Kuhlmann and her co-conspirators began a seven-day siege – demanding $5 million and the release of 53 Palestinian and Pro-Palestinian militants for the release of the hostages, many of whom were Israeli.

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A member of the German-based Revolutionary Cells, Kuhlmann was a tough prospect for Pike. Encouraged by her director José Padilla, she took a crash-course in German to speak some of her lines in Kuhlmann’s native language. “He said, ‘Can you do it?’ I said, ‘OK, sure. Let’s try.’ Then we came over to Berlin and we got a coach, José said, ‘Is this possible?’ And she was very, very doubtful!” She studied furiously. “[Actors] are good at that,” she shrugs. “You can ride, you can surf, you can do an accent.”

Acting in German is one thing. But Pike had to find her way into the mind of Kuhlmann, who died when the Israeli Defense Forces stormed the airport. “There’s a surprising deficit of information. You look up Brigitte Kuhlmann and you get one or two pictures; this rather hostile-looking strange blurry image of a woman with short dark hair and glasses.” During the making of Entebbe, Kuhlmann’s former lover released another photo of her on Facebook. “It was such a different image, of an innocent looking younger woman,” says Pike, who struggled to reconcile the two.

What the film does well is chronicle the pressure-cooker situation that she and fellow German Wilfried Böse (Daniel Brühl) find themselves in, when they team up with two members of the Popular Front for the Liberation of Palestine. One scene in particular, showing Kuhlmann cracking at the seams during a phone conversation, lives long in the memory. “You see the [mental] fragmentation,” says Pike. “What happens to a mind under that kind of pressure?”

Starring in Entebbe represents yet another impressive marker in Pike’s career. She’s always shone, right from when she was 21 and cast as the icy Miranda Frost in her 2002 feature debut, James Bond movie Die Another Day. But she was rarely given the chance to express herself. Instead, she played back-up to male A-List stars: Johnny Depp in The Libertine, Tom Cruise in the Lee Child adaptation Jack Reacher and even Dwayne ‘The Rock’ Johnson in the ill-advised sci-fi Doom.

Only occasionally, like her endearingly silly girl in An Education, were there glimpses of what Pike was capable of. If there was a turning point it was 2014’s Gone Girl. David Fincher’s adaptation of Gillian Flynn’s scorching best-seller about murder and marriage, Pike’s casting as the unhinged author Amy Dunne won her an Oscar nomination. Perceptions shifted. “Even fan letters – they’d say, ‘I was so worried when you were cast, I thought you were way too sweet but God was I wrong!’”

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Since Gone Girl, Pike has been pushing boundaries, experimenting wherever she can. Like the eerie music promo for Massive Attack’s Voodoo In My Blood that sees her hypnotized by a floating silver orb. Or last year’s Hostiles, in which she played a 19th Century American who loses her whole family in a brutal Comanche Indian attack. What’s put her on this path? “Freedom, I suppose. I know that the only good acting really comes when you’re free. It’s a chance to something that could potentially fail.”

Acting was always something she craved, even as a child. “Since I was really small I knew it, but I don’t quite know why.” Born in upmarket Hammersmith in London, her own upbringing was steeped in the arts. He parents, Caroline and Julian, were both concert musicians, and Pike spent her early years watching them from the wings. But it wasn’t for her. “Music just wasn’t the way I wanted to express myself. In music, you still have to be yourself. If you’re performing, you’re still you. And I liked being other people!”

Her education was first-rate: she attended Badminton in Bristol, where Iris Murdoch also schooled, then won a place at Wadham College, Oxford, to read English. A contemporary of Chelsea Clinton, she finished with a 2:1, though not before she’d detoured to apply for every drama school going. Rejected by them all, she had to return to Oxford and grovel to finish her degree, which she only concluded part way through shooting Die Another Day; at least she could lay claim to being the first Bond girl to graduate from Oxford.

Even then Pike had her eyes on the prize, wanting to emulate the raw emotion Emily Watson managed in Breaking the Waves. Now she’s in that position: every role a hard-fought gem. Away from the camera, if she’s not changing her fringe, she retreats into her shell. “I go very private. I’m not very at ease in social situations and parties. I’m not a socialite at all. I always feel very uncomfortable...I’m fascinated by people who find that very easy. I can do it when I’m promoting a film but other than that...”

She trails off. Quite how she’s found time to raise two young boys – Solo, 5, and Atom, 3 – with her husband Robie Uniacke is a mystery. “It’s been pretty non-stop recently, because the prep for these roles is so massive,” she acknowledges. This includes chemistry lessons at her house to play Marie Curie. “After [playing] Marie Curie, I’m going to take a break, a proper break,” she says. Well, until the next killer role comes along.

Entebbe opens on May 11.