There are secrets, and then there are secrets. With all the carefully recalibrated stories about drug excesses and sexual high jinks during the recording of the Rolling Stones’ 1972 album Exile on Main St, it’s hard to believe there could be anything that Mick Jagger, Keith Richards and the rest of their band of groovy, deeply grooved superstars could possibly have to hide or be ashamed of. So it’s astonishing to discover that, for nearly four decades, the Stones have vigorously enforced a strict legal injunction banning the screening of a documentary about them, a film some of the few people who have seen it think is a masterpiece.

Called Cocksucker Blues, after a raunchy Stones song of the same title that Jagger dared the record label to release (it didn’t), the documentary was mainly shot during the Stones’ 1972 tour of North America, just after they had released Exile. It was directed by the photographer turned avant-garde film-maker Robert Frank, best known for reflecting 1950s America back at itself in the collection of street photography titled simply The Americans. Frank, a Swiss Jew born in Zurich in 1924, had emigrated to America in 1947. The grainy black-and-white cover of the Exile on Main St album is one of his works.

Under the terms of the injunction, which Frank fought at the time, CS Blues can be shown only a limited number of times a year. The photographer, who is now 85, has been a virtual recluse in Nova Scotia for the past few decades. He owns one of the only two prints of the film; his is reportedly unprojectable now. The Stones own the other print. One of the rare contexts in which it has been legally shown in the UK was during a retrospective of Frank’s work at Tate Modern in 2004, where it was screened eight times. Until recently, when pirate copies began appearing on the internet, the few people who had managed to see the film had watched it on bootleg VHS videos of dubious quality and provenance.

In part because of its outlaw cachet, CS Blues has become an iconic “text” in the history and mythology of the Rolling Stones. The film even appears as a short chapter in Underworld, Don DeLillo’s 1997 novel about the cultural history of 20th-century America. Nick Broomfield, the English documentary film-maker, who rates the Stones as his all-time favourite band, first saw it at a rare screening at an art-house cinema in Los Angeles in about 1980. Well, part of the film.

“It was a big cinema, and it was completely full,” recalls Broomfield, who has made documentaries about Kurt Cobain and the rappers Biggie Smalls and Tupac Shakur. “About half an hour into the film, these stink bombs, smoke bombs, went off, and they cleared the cinema. The story going around was that the Stones didn’t want the screening, and that somebody had deliberately let these things off. Who knows?” It was another two years before Broomfield managed to see the rest of the documentary. His verdict was, and remains, unequivocal. “I think it will survive as one of the greatest rock’n’roll films ever made,” he says. He believes it’s on a par with Don’t Look Back, the documentary made by DA Pennebaker about Bob Dylan’s 1965 British tour. “Any documentary film-maker would have been exceptionally proud to have made it.”

The 1972 North American tour was important for the Stones, and was shaping up as a big cultural event, with celebrity writers such as Truman Capote covering it. Their tour of America in 1969 had culminated in mayhem and murder at the Altamont Free Concert, events captured in brutal detail in the documentary Gimme Shelter, which showed a member of the Hell’s Angels security detail at the concert stabbing a man to death. The Stones hired Frank, then 47, to cover the new tour vérité-style, partly because they liked his photography, but also because they were admirers of his 1959 avant-garde documentary Pull My Daisy, which was adapted from a play by Jack Kerouac and had an improvised narration by the Beat writer.

It’s hard to know whether or not the Stones really understood what Frank was up to. According to Susan Steinberg, who edited the film: “He had no interest in the music at all. He hired a separate crew to film the music sequences.” Frank used three kinds of cameras, including one left lying around for anyone in the Stones or their large entourage to shoot with. Starting as the band were mixing Exile in LA and finishing some two months later with the final concert at Madison Square Garden, in New York, Frank, and others, including Jagger, shot about 25 hours of footage.

As Steinberg discovered when she started editing, a lot of it was of poor technical quality, because one of the film magazines had a light leak in it. Not that it bothered Frank. She says that as she started watching the footage, she found herself “drawn into how Robert saw things, how he experienced their world. I felt like I was there with them”.

And that, through the fractured, grainy, loose, swirling images and deconstructed sound, is how the finished film comes across. (I have seen a pirated version.) We feel we’re there, hanging with the Stones and their entourage — backstage, in hotel rooms and corridors, in planes between cities, in cars between gigs. We feel we’re getting a visceral sense of what it must really have been like to be in and around the world’s biggest and baddest rock’n’roll band, at a time when that really mattered. While many scenes feature nameless members of the endless entourage, Frank’s documentary is also spattered with socialites eager to get close to the flame, including a bored Bianca Jagger, whom Mick had recently married, and who had her own posse, and Princess Lee Radziwill, younger sister of Jackie Kennedy.

So why is CS Blues so controversial? Where to begin? The film shows things that are only hinted at in most documentaries, including The Stones in Exile, the group’s new sanitised, self-produced documentary about their sojourn in France making the album, shown recently on BBC1. (The Stones in Exile includes about 10 minutes of judiciously selected outtakes from Frank’s footage.)

Frank casually shows people shooting up heroin, including a beautiful young groupie in a hotel room choking off her veins and plunging a needle into her arm as Richards watches. He shows Jagger snorting a large mound of cocaine off a switchblade; Jagger filming himself in a mirror, with his hands down his tight pants, starting to masturbate; a groupie lying on a bed, her legs spread, rubbing semen into herself; Keith rolling up a dollar bill to snort coke. And, in the most disturbing scene, two groupies being jostled by roadies on a plane, then having oral sex performed on them as Jagger and Richards look on, nonchalantly banging tambourines.

“I didn’t censor anything,” says Steinberg, who was just 22 when she edited the film in Frank’s loft in the Bowery, New York. “I went for the blood and the guts, the sex, drugs and rock’n’roll. I saw quite clearly that it was a film about being behind the scenes, not about what’s on stage; about being on the road, being back in those hotel rooms with them, seeing the underbelly of the boredom, the ennui, the drugs, the girls.”

At first, says Steinberg, Jagger seemed happy with it. “At that time, they loved being the bad boys, so this film was a direct expression of how they perceived themselves.” But the Stones and their lawyers were worried that such open drug use, in particular, might get the band banned from America, so the film was shelved. Then, in 1977, Steinberg got a call from the Stones saying that they were keen to see if a re-edited version could be released. Steinberg says she simply shortened some scenes. I ask whether she took out shots of Richards shooting up heroin. “Well, this is going to be printed, and they’re going to kill me, so I don’t know quite what to say,” she says.

It’s many, many years later, I say.

“I know. Many, many years,” she says. “Look, I can’t remember the exact shot, but it was clear that Keith had shot up. Even now, in the film, you see that scene of him nodding out in the dressing room, going lower and lower into that girl’s lap. It’s quite clear that he was using heroin.”

While Steinberg was recutting the film, Richards was busted for heroin in Toronto. One of the Stones’ lawyers came to see it and said, Steinberg recalls: “‘There’s just no way you can show this film.’ And that was that.” According to the late Allen Ginsberg, a friend of Frank’s, Jagger told the director: “It’s a f***ing good film, Robert, but if it shows in America, we’ll never be allowed in again”

While that may have been a valid justification for keeping the film under lock and key at the time, it can hardly be now. I mean, the Stones have even played the Super Bowl. The truth may be that what troubles Jagger and the band is that CS Blues so ruthlessly deglamorises what the Stones have always been so keen to mythologise, their “elegantly wasted” rock-star lifestyle. Instead, Frank shows us a world that is “empty and dehumanising, a blur of people in rooms, waiting for the time between gigs”, said one writer, making being in the world’s biggest rock’n’roll band “look like such a soul-destroying, achingly empty hell”. As DeLillo puts it in Underworld: “The camera phalanx in the tunnels. People sitting around, two people asleep in a lump or tripped out or they could be unnoticeably dead, the endless noisy boredom of the tour — tunnels and runways.”

Broomfield is exasperated that people should be judgmental about what Frank shows in CS Blues. “I don’t think you can look at it as a bleak vision,” he says. “Maybe that’s why the Stones don’t want it out, because they are worried that people will judge it like that. It is a complex portrait of some really brilliant artists, of people who are pushing the boundaries in all areas, an amazing portrait of the greatest rock’n’roll band ever at the height of their creativity. It is what it is.”