There is a wonderful photograph of Seretse and Ruth Khama sitting together on a rocky hill above the plains of what would later be renamed Botswana, with Seretse as its first president. You can’t see his eyes behind his aviator sunglasses, but you can see a slightly pained look in Ruth’s, as well as a defiance in her clasped hands. The marriage, less than two years earlier, of a white British woman to the heir to the leadership of Bechuanaland’s largest tribe was opposed by just about everyone – their families, Seretse’s Bamangwato people, the British government (which held Bechuanaland as a protectorate) and the South African government, which couldn’t countenance an interracial couple leading its neighbouring country.

For years, the actor David Oyelowo had been trying to get a film about their story made. When he approached Pike to play Ruth, he sent her this photograph. “In those faces close together,” she says, “I saw the love and the cost all at once – and I started to cry. It was a strange reaction, not a normal reaction for me.”

The clerk and the king … the shot that helped persuade Pike to star in the film. Photograph: Margaret Bourke-White/Getty

It is an extraordinary story. Ruth was a clerk at Lloyd’s underwriters when she met Seretse, a law student at Oxford, at a Missionary Society dance in London in 1947. They fell in love and married the following year, despite attempts to derail their romance. In Bechuanaland, where Seretse returned to take up his kingship, the couple were also met with hostility. Under pressure from South Africa, which had just set up apartheid, Britain exiled Seretse from its protectorate. Ruth stayed in Bechuanaland, where she gave birth to the first of their four children before joining him in England. They were allowed to go back to Bechuanaland in 1956, where Seretse founded a political party, eventually becoming president of the newly independent Botswana.

Pike read old newspaper reports in the British Library that sensationalised their relationship as one of forbidden love, with Ruth cast as the London typist who became a “white queen” in Africa. “She didn’t court it in any way,” she says, when we meet in a London hotel. “Imagine you’re dating a man and you find out this is his heritage.”

Pike is a slightly unnerving person. She is flawlessly beautiful, her voice soft and low, the way you would speak to a spooked animal. She seems both youthfully naive and about 100 years old. She says the story spoke strongly to her. “I’ve often felt I don’t belong quite wherever I am. So someone fearless like Ruth moves me. The fact she never wavered is very inspiring.”

Their tale is told in A United Kingdom, out this week. It was wonderful, says Pike, “to play someone who’s nobler than you, more heroic. I think she was one of those women who was liberated utterly by the second world war. She suddenly saw opportunities for women. I think I was channelling some of the spirit of my grandmothers. I remember when they talked about the war – I had one grandmother who worked in radar. You’re given a position that matters, your decisions and readings of situations matter, and all that was pretty new for women. It was exciting and there was pride in it.”

Ruth Williams, as she was, had driven ambulances at Friston airfield, where stricken British and American planes landed. Pike read the accounts she had written. “She’d be listening to the pilots on the radio: ‘Coming in now, I’m not sure the old girl’s going to make it.’ And her heart would be in her mouth. Sometimes the plane would land and burst into flames, sometimes the pilot would come out grinning. She was on the front line of life and death. I feel that, after that, everything was absolute for her. The certainty. I think she felt something so huge for Seretse and thought: ‘If I let him go, I might never feel this way again.’”

Directed by Amma Asante, A United Kingdom is only the second time in Pike’s film career – which started in 2002 with Die Another Day and has included everything from independent films to blockbusters – that she has worked with a female director (the previous one being Lone Scherfig in An Education). Isn’t that rather surprising? “I know,” she says. “There aren’t very many.” She remembers speaking to a woman who had directed a successful film, but had then worked in TV. Pike admits to wondering why. “You get suspicious. Then I met her and she said: ‘It’s frustrating – everyone assumes I’ve had some sort of flop, but I’ve just had a kid and decided I didn’t want the length of time and commitment that a feature takes.’ And you think: ‘Ah, of course.’ People are so quick to read into a woman’s career that something bad must have happened.”

A similar thing happened to her after the huge success of 2014’s Gone Girl, the adaptation of Gillian Flynn’s bestselling thriller, which brought Pike an Oscar nomination for her role as Amy Dunne – and shredded any remaining ideas that she was just a pretty, posh English actor. Her career also appeared to have a dip, but she had actually just had her second child with her partner, businessman Robie Uniacke. “It was pretty powerful being Amy,” she says. “I think I wanted to be very human for a while, very maternal probably.”

‘It was powerful being Amy’ … Pike with Ben Affleck in Gone Girl. Photograph: Allstar/New Regency

This proved rather hard, given the explosion of interest. “It was a big moment and also surreal,” she says. One magazine wanted to do a day-in-the-life-of-an-Oscar-nominee shoot, picturing her by the pool or getting her nails done. “I was like, ‘Are you joking?’” She laughs – a more accurate picture would have shown her carting the baby carseat around or struggling with bags of nappies. On the day the news of the Oscar nominations broke, she had to do phone interviews while lying on her bed, trying to entertain her two young sons at the same time.

Men don't want to play second fiddle to a woman

There were lots of offers: she was cast in a film with Christian Bale, but it was shelved when he hurt his knee. Then she did HHhH, playing the wife of Reinhard Heydrich, the senior Nazi behind many Third Reich atrocities. She played a CIA agent in High Wire Act, a political thriller set in 1980s Beirut, and did another Christian Bale film, Hostiles. All are due to come out next year.

But none are leading roles. She is either playing the wife, or a supporting character to the male leads. Was Amy Dunne a bit of a rarity in being a compelling female lead? “She is, but maybe I’m quite comfortable being No 2. I quite like that place. I don’t know that I’m that easy with being No 1.” Why? “I suppose you feel there’s somewhere to go. It’s an interesting question. I haven’t analysed why.”

Pike has been working on getting a passion project off the ground for several years, in which she will play the lead. “It’s not easy casting the men,” she says. “You have to go gingerly but you have to approach the right man at the right time, because men don’t want to play second fiddle to a woman. That’s the truth. It’s sad, isn’t it? Christian [Bale] might be different – he’s a leading man who quite wants to be a supporting actor, and is quite unusual in that respect. But … ” A pause, then a resigned: “Yeah.”

Her comfort in second billing may also, she says, be rooted in self-doubt. “You’re carrying the movie when you’re No 1,” she explains, “and I don’t know that I’m ready for that yet. I should be.” I point out that she carried a huge movie, Gone Girl, or at least did so equally with Ben Affleck. “I don’t know,” she says, looking a touch embarrassed. “Ben was still No 1 on the callsheet. The guy’s usually No 1.”

It’s the stories that interest her, she says, so if that means taking a smaller part, why should it bother her? She doesn’t feel she has to be the star? “No! God, no. But I probably should. I’d probably be more successful if I did. It would probably be a good idea.” She laughs. “Yes, note to self: go home and read scripts where female character is the lead.”

• A United Kingdom is in cinemas from Friday

• This article was amended on 23 November. The original said that Amma Assante was the first female director with which Pike had worked. In fact she is the second.