Boxing was there at the very dawn of cinema. As early as 1894, film-makers were shooting prize fights: the fast and furious physical spectacle was perfect for the new medium of motion pictures. Soon, scores of directors had been drawn to boxing – not just for the violence but for the drama of fighters' lives. In 1927, Hitchcock made The Ring, a silent tale of a pugilistic love triangle that is his one and only original screenplay. While many boxing movies reached greatness, even the most ordinary could still thrill with a canny sprinkling of what became genre staples: wise old trainers, crooked promoters, fixes, comebacks, wives who can't bear to look. In fact, plenty of boxing films are really about the women behind the men.

To tell the story of the boxing movie in a one-hour documentary is to know, just fractionally, the struggle of the fighter trying to make the weight, ruthlessly boiling down. But when the chance came to make Boxing at the Movies, I grabbed it – not just as a film-lover. As a kid, I'd been glued to the fights of British flyweight Charlie Magri, who could knock opponents out with either fist and didn't bother too much about defence.

Nicknamed the Brown Bomber and considered one of the greatest heavyweights of all time, Joe Louis inspired movies like 1939's Golden Boy, based on the Broadway play by Clifford Odets. In a somewhat unlikely scenario, it followed the fortunes of Joe Bonaparte, who dreams of becoming a great violinist by using the money he can earn as a boxer. But will he damage his hands in the process? On stage, the cast included Elia Kazan and the teak-tough John Garfield. The latter would go on to star in 1947's Body and Soul, a bristling allegory about an ageing champ and crooked promoters, before he was blacklisted in the anti-communist witch-hunts of the 1950s. And a namer of names during those denunciations was one Elia Kazan, who went on to direct the bleak 1954 classic On the Waterfront, in which Marlon Brando's boxer turned bum famously declared: "I coulda been a contender." That same speech would be recycled by Robert De Niro's Jake LaMotta in Martin Scorsese's gory 1980 epic Raging Bull.

While filming in New York, it was hard not to bump into the past. One sunny afternoon, we ate fancy burgers on gentrified Rivington Street in the Lower East Side. In the 20s, it had been a slum – home to street kids including John Garfield and future middleweight champion Rocky Graziano, considered one of the greatest knockout artists ever. By 1956, Graziano would have his own Oscar-winning biopic, Somebody Up There Likes Me, starring Paul Newman and directed by Robert Wise – who had already made boxing's pulp masterpiece The Set-Up, a 1949 film about boxing's dirty underside, which was adapted from, of all things, a jazz-age poem by Joseph Moncure March. Although the poem's protagonist is black, the film features Robert Ryan in the role.

Actors playing fighters have been willing to spill their own blood in order to make a film feel more real. After De Niro in Raging Bull came Daniel Day-Lewis, who prepared with typical rigour for 1997's The Boxer by getting cheerfully pasted up and down London's legendary Fitzroy Lodge gym. But traffic goes the other way, too: the long line of fighters turned film stars includes Carl Brisson, star of The Ring, as well as London schoolboy champ Ray Winstone.

There are times, however, when boxing and movies don't get on so well. In Scorsese's screening room, Raging Bull's editor Thelma Schoonmaker told me how much she and Scorsese disliked the fight game. And at Fitzroy Lodge, trainer Mark Reigate and fighter Pop Khan said boxing movies too often demonised the sport they love. Their favourite exception? When We Were Kings, the euphoric, era-defining account of Muhammad Ali's 1974 Rumble in the Jungle with George Foreman, in what was then Zaire – a bout few expected Ali to win.

Will the love affair ever end? Well, just after we finished filming, a green light was confirmed for Grudge Match, a boxing comedy in which De Niro and Sylvester Stallone play greying rivals. Raging Bull and Rocky in the same ring? It's an idea that could only have come from one of two sources: a film producer or a fight promoter – kindred spirits, as ever.