'The wild nights, the orgies, the drug-taking. I remember it well," reflects Mick Jagger on those much mythologised months that The Rolling Stones spent in the south of France in 1971 recording one of rock music's greatest albums, Exile on Main Street. One of the most debauched, drink-sodden, drug-addled collection of songs going, Exileis not just a summation of the counter-cultural 1960s, but also a portent of the rock cliche-ridden 1970s to come.

The backdrop to the album wasn’t pretty: a nearly bankrupt band retreat to the heroin-addicted guitarist’s house (full of hangers-on, dealers and the various forms of human detritus who attach themselves to seedy fame and glamour) for a series of farcical recording sessions. Couriers bring a steady stream of drugs, PG Tips and HP sauce. Band members are unable to be in the studio at the same time, nobody seems to be playing their allotted instrument. A group of Bengali drummers is summoned – they take one look at the shambles

and turn on their heels. There was no power supply, the guitars were warped by the oppressive heat, and William Burroughs, Gram Parsons and other “faces” upped the distraction quotient.

When they emerged from this swamp some months later (forced out by Richards being banned from France for two years), all they had was a series of tapes and a severe comedown.

“It seemed like we were in the south of France forever” says Jagger, “but it was actually only six or seven months. There was quite a bit of socialising and carrying on. It was great fun. It got a bit out of hand. Then we left.”

Playing back the tapes, they found, as Jagger recounts in a new, bare-all documentary film of the making of the album, "that what we thought was truly atrocious was actually wonderful material". The film, Stones in Exile, which premiered in Cannes on Wednesday and is on BBC1 on Sunday night, is a superb anti-morality tale.

Judged to be a ragged mess on its release, radio wouldn't touch the album (apart from the single Tumbling Dice) and The Stones rarely give any of these songs a live outing. Like Astral Weeksand Pet Sounds, it has grown hugely in stature over the years, and is now a touchstone of sorts for anyone from Primal Scream to The White Stripes.

Thirty-nine years later (and with a new version containing previously unreleased tracks in the shops), the band are still reliably fractious about their memories. Jagger remains baffled by the album’s critical success (mainly because it’s the most Keith Richards Stones album there is), even suggesting that he helped “rescue it” at the mixing stage in a Los Angeles studio.

When this is put to Richards, the guitarist replies: “Mick’s recollection is quite honestly bullshit. He doesn’t feel under any obligation to tell the truth.”

The decadent aura of the album – which props up the fallacy that drink and drugs facilitate great art – is prosaically dismissed by Jagger now. “It was just the lifestyle then,” he says in the documentary. “Yes, there was drugs, drinking and carrying-on, but that was the rock’n’roll environment of the day.”

Despite the extracurricular activities, the band did get it together (musically speaking). For Jagger the circumstances behind the album were the real spur.

“We had no money – and I mean no money whatsoever. We were run out of England because we couldn’t pay our taxes, so we had to get out of the country to pay the money we already owed. We thought we would never be able to work in the US again because of all the drug busts against us. We didn’t know what to do or where to go.

"We were literally exiles – it was us against the world on Exile on Main Street."

The Stones in Exileis on BBC1 Sunday at 10.45pm, followed by the 2006 concert A Bigger Bang: Liveat 11.50pm