In 1955, when she was 12 years old, Billie Jean King says she had an epiphany. “I was daydreaming about my little tiny universe of tennis, and I thought to myself: ‘Everybody’s wearing white shoes, white socks, white clothes, playing with white balls, everybody who plays is white. Where is everybody else?’” she recalls. “That was the moment I decided to fight for equality and freedom and equal rights and opportunities for everyone. Everyone. Not just girls. Everyone.”

Now, 62 years later, the most sensational moment of her long, boundary-smashing tennis career has been turned into a film. Directed by Little Miss Sunshine’s Jonathan Dayton and Valerie Faris, Battle of the Sexes tells of the run-up to that infamous high-stakes 1973 match between King (Emma Stone) and the showboating, self-confessed “male chauvinist pig” Bobby Riggs (Steve Carell), in front of 30,000 live spectators and a colossal Superbowl-sized TV audience. But those expecting a straightforward sports movie may be surprised by its intimacy, as it draws a parallel between the weight of having to prove the worth of all female athletes in that one match, and the distress of hiding a secret affair with her female hairdresser from both her husband Larry and the world.

When meeting King, it is obvious why she has been at the vanguard of so much change, having dedicated much of her life to the fight for equality. When the men’s tour refused to address women’s concerns over pay disparity, King broke away to set up a women’s tour, with each of the “Original Nine” players signing a symbolic $1 contract (it is a barnstorming moment in the film, although the timeline has been loosened somewhat to fit dramatic demands). Shortly afterwards, she founded the Women’s Tennis Association. But when President Obama awarded her the Medal of Freedom in 2009, he praised “all the off-the-court stuff – what she did to broaden the reach of the game, to change how women athletes and women everywhere view themselves, and to give everyone, regardless of gender or sexual orientation – including my two daughters – a chance to compete both on the court and in life.”

King with 55-year-old Bobby Riggs ahead of the match. Photograph: Bettmann Archive

In person, she is a brilliant and invigorating livewire, hands knitted together, leaning in to answer questions long before they are finished. She practically sparks with enthusiasm. She has a boundless curiousity about what other people believe, and before the hour is up she has discovered how old I am, where I grew up and what it was like. She is adopting the word “queer” because young people tell her they prefer it to “gay” (“although I still feel gay. You know why I like it? Because it’s happy, happy, happy”). She genuinely wants to know why: why did millennials not trust Hillary Clinton? Why did women, any women, vote for Donald Trump? She slaps her hands together gleefully when she hits on a point she wants to emphasise, which is usually a life lesson about how people can be more kind to one another. At times, chatting to her is like being in a one-on-one TED Talk. Her positivity is utterly contagious.

The story of the Battle of the Sexes match is familiar, thanks to its place in the history of sport and the many documentaries that have been made about it, but some of its more gruesomely misogynistic details are shocking for a modern audience, not least the complete refusal of the tennis establishment to take the idea of a professional women’s game seriously. King is pleased that parts of the film will alarm a younger generation, for whom she has a great deal of respect. “I’m really optimistic about millennials,” she beams. “And the Gen Z, I don’t know what you call them here – the ones that are 18, 19 now.”

In 2014, King founded the Billie Jean King Leadership Initiative, a non-profit organisation dedicated to promoting equality in the workplace. She says that, based on research it has carried out, “this is the greatest generation on inclusion ever. And that gives me hope. We’ve done all kinds of studies and it holds true that young people don’t want to be in a workplace that doesn’t have inclusion. They’ll leave work and go to another company if it has better inclusion.” She starts to rap on the table, delivering a speech. Diversity is absolutely vital to her worldview. “I think the kids that are younger are going to learn from millennials, and pick up on that, too, and I think this could probably save the world.”

She says this with such certainty that it feels mean-spirited to cast doubt on it, but I wonder if she still feels optimistic when the political establishment in the US and the UK feel so far away from that ethos. “But some of the people in the establishment believe in inclusion, so you have to look at each person.” King is big on trying to see the best in everyone, although she admits that, in one respect, during the 2016 presidential election, young people disappointed her – she feels they didn’t use the internet as a research tool. “These kids didn’t know one thing about Hillary. Not one thing. They only knew that Bernie was yelling ‘revolution!’ and ‘free education!’. I’m like: Really? What’s his policy to pay for the free education? ‘I don’t know.’ Well, you guys, it takes money. All these things that you want, they take money. You’ve got to be a little deeper in the weeds on this. Oh, my God,” she says, exasperated. “I would have given anything to have this technology at my fingertips. I would have loved it as a young person. But, use it! They didn’t use it for the elections, not at all.”

King is carried to the court for the Battle of the Sexes tennis match. Photograph: Bettmann Archive

Last month, King gave an interview that touched on Trump and said: “I’m upset with the white women that voted for Mr Trump. I think they really don’t like themselves.” The quote was widely reported, but she seems mortified today, calling it “my biggest faux pas ever”.

“Oh, you know what? I got that all wrong. It sounds so sexist. It wasn’t about sexism – it was about gender. We were discussing the election and, of course, I got one little soundbite and I blew it on that. That was a big mistake I made. Of course I don’t know what each person thinks. It was a statement, but it was a question. How can any woman vote for Trump anyway, in my mind? I’m just asking myself questions.” She regrets the way she worded it then, but she is still asking the question now. “When you heard him say all those things on the bus about women and how you can grab ’em? How do you justify that? I just wanna ask.”

One of King’s many big theories about life is that, through sport, women can learn how to navigate a world built by men. “Men created the culture, not women, not really,” she says, matter-of-factly. “If you’re in sports, you learn [about] the old-boy network. You learn how they think. It gives you a leg up every time. The lessons you learn in sports, you can use in your daily life. I use it every single day of my life.”

During the early rounds of promotion for Battle of the Sexes, King sat down with Emma Stone and Andrea Riseborough – who plays her hairdresser and lover, Marilyn Barnett – for a three-way interview. Stone mentioned that women were making 80 cents to every dollar earned by men, and King gently interrupted: “White women. If you’re African American or Hispanic, it goes down, and then Asian American women make 90 cents to the dollar.” The internet applauded her intersectional feminism; Refinery29 compiled a video called “Woke Moments from Billie Jean King”. “Yes! That’s great. They understood that.”

It was a black player, Althea Gibson, who changed King’s view of what being a winner meant. “I think you have to see it to be it. Althea Gibson was the first woman of colour to ever win a major. In ’56, she won the French, ’57 and ’58, she won Wimbledon. I got to see her as a 13-year-old and she changed my world because I knew what it looked like to be No 1. She inspired me more than ever.”

Emma Stone and Steve Carrell as King and Riggs. Photograph: Melinda Sue Gordon

Growing up in Long Beach, California, she was certain tennis would be her weapon. “It would give me a platform, if I was good enough. I’d have to be No 1 and I knew as a girl it wouldn’t be the same as a guy – it’s going to be harder, it’s going to be different. It is. We go unnoticed.”

King was a religious teenager, and her parents were homophobic. “I wasn’t comfortable in my own skin until I was 51,” she says. “It was a long haul. The movie was kind of the beginning stages of what I was going through.” The sense of pressure on screen is palpable. “Oh, so much pressure, to not be ‘like that’. And I love Larry. I married him thinking I was totally straight. He’s so gorgeous. He was gorgeous. We both were, I guess. Have you seen old photos of him?”

The conversation turns wonderfully gossipy. “You wouldn’t recognise him or me now. I fell in love with him across a room. I still would, probably. I don’t know. I either like ’em really dark or really light. Ilana [King’s partner] is dark, my first boyfriend was really dark. Then Larry was blond. I’m either one extreme or the other. I don’t really understand it.” Did it take her by surprise, then, to realise that she was attracted to women? Did she have no idea? “I know a person who was with a guy and had two children, and [thought] she was totally straight. She was in her 40s, and now she’s with women. That happens a lot. Or, I think more of us are fluid and can be with either. And they’d say: ‘That’s bisexual.’ Well, I don’t know. I’m with Ilana – it’s going to be 38 years in October, so to me I’m a lesbian right now. If something happened to Ilana, I don’t know, I’m always open.

“I prefer looking at men’s bodies, though,” she confides. “I think women, it’s more of an emotional thing. It’s physical, but it’s different. Whereas men’s bodies, I love broad shoulders, I love that look. So, I don’t know. I’m not sure. I’m a little screwed up, but it’s all right. At least I’m open to everybody.” It’s her openness that makes King so persuasive; she is open to what everyone has to say, including her enemies. But then, you don’t get to be the best female tennis player in the world without learning how to read your opponents.

King holds her trophy high after beating Riggs. Photograph: Bettmann Archive

In 1967, when she was 23 and at No 1 in the rankings, King was profiled by the New York Times. Even then, she was rallying against the stuffiness of the tennis world. “Oh, totally. I’m always getting into trouble,” she says. The writer referred to her as “an ordinary, attractive young lady”, and she laughs at the description. “Take lots of photos in your 20s, save ’em, cos when you’re old and wrinkly you can look back on ’em and go: ‘Ah, I looked pretty good then.’” She catches herself. “But we’re talking about body image again! Do guys think like this? I think guys do, a little bit more than they let on.” She is pleased that, 50 years ago, she was complaining that the elitist “club atmosphere” was damaging to the sport and that it needed to be brought into public spaces such as parks, where everyone could feel welcome. She sounded remarkably contemporary. “That’s what you have to do, be ahead of your time. Be ahead!”

King is hoping that the love story at the heart of the film will help others in areas where she could not be ahead of her time; as she says, she spent a number of years denying her sexuality. “I hope [it] helps motivate kids, young people, to fight for equality and freedom, and for the LGBTQ+ community …” She speaks the letters carefully, and then happily veers off track. “I say ‘plus’ because there are so many letters now, I can’t keep up. We have this Q now, it’s ‘questioning’ or ‘queer’. In my day, that would be the worst thing you could say. But I asked the younger ones, what do you like, and they like ‘queer’ now. So I’m starting to use ‘queer’, because they’re our future leaders.”

The film is a stark reminder of how much King was up against then, and how much women are still having to fight for recognition now, whether it is John McEnroe’s comments that Serena Williams would be “ranked, like, 700 in the world” in the men’s game, or Novak Djokovic stumbling over “the hormones and different stuff”. King would like it to be of use to others. “Maybe it will help them come out, but only come out when you’re ready,” she insists. “Do not out people.” In 1981, Marilyn Barnett sued King for what the tabloids salaciously called “galimony”, and outed her in the process. King lost her endorsements; the backlash was so strong as to be barely conceivable today. “Young people today are probably like: ‘Are you kidding?’ But even gay kids, or queer kids, didn’t talk about our situation among ourselves. It was totally shame-based.”

Her Australian contemporary, Margaret Court, has also been openly hostile. A minor character in Battle of the Sexes, she is now a pentecostal pastor in Perth who has said that “tennis is full of lesbians” and that gay people are “after our young ones”. King smiles, although the two were once friends. “[Margaret] believes in conversion, that if you’re gay you can turn around. Not happening, nice try. No. We’re all God’s children – accept us the way we are, as long as we’re not hurting others. When she said that trans children are from the devil – you don’t do that. Don’t hurt my community like that. I think we need to have a hard talk, and ask hard questions.”

Hard talk and hard questions seem to be what King thrives on. Still, she isn’t sure quite why she has spent much of her life trying to change the world. “I don’t know. I’ve always been this way, since I was a kid. It’s just, do you want to build goodness and a better world, or do you want to tear it down? You decide.”