Some real-life stories are such a narrative gift for documentary makers you wonder why they weren’t filmed years ago. Co-directors James Erskine and Zara Hayes’ engrossing doc about the efforts of a few, pioneering female tennis players to bring sexual equality to the sport is one such story.

It takes place at the time, the late 1960s, when tennis became a professional sport. The enormous gap between the prize money awarded to male and female players made it clear just how unequal the game was, and it underscored the old prejudices that saw female players regarded as unfeminine.

Erskine and Hayes have set this shameful period of tennis against the broader backdrop of the women’s liberation movement. They focus on Billie Jean King, the tennis star who had been married for several years, who was to come out as lesbian (though, appropriately, little is made of that here), who was widely admired for her sporting ability and who was an outspoken proponent for women’s rights.

It was King, along with a small group of other female players, who parted ways with the United States Tennis Association to start their own tour, a protest move that could have cost all of them their careers. What it did instead was bring King and her companions to the attention of Bobby Riggs, an ageing tennis champ and self-confessed chauvinist pig who saw an opportunity to rekindle his career by humiliating female players on the court.

What followed was a high-stakes game between King and Riggs that gives the film - which really benefits from a wealth of archive footage and a great soul soundtrack - its title and a climax that’s just as thrilling as the Ali/Foreman Rumble in the Jungle that came a few years later.

Screening at the Dominion, Fri 21 Jun and Cineworld Fountainpark, Sun 23 Jun, as part of Edinburgh International Film Festival 2013. Limited release from Fri 28 Jun.

The Battle Of The Sexes official trailer