I can’t off the top of my head think of another instance where you’ll find a former US President queuing up alongside the head of the Hell’s Angels to dispense hosannas on one man. But that, perhaps, says much about Hunter S Thompson’s influence on American culture – particularly during the late Sixties and early Seventies when, as Alex Gibney’s brilliant documentary rightly identifies, Thompson was, unbelievably, one of the most influential men in the country.

Gibney’s film opens though with 9/11 and fast-tracks to Thompson’s suicide in 2005. Gibney draws parallels between George W Bush and Thompson’s bete noir, Richard Nixon. Several of Thompson’s best-known quotes, originally directed at Nixon, could easily be applied to Bush Jr: “He was a cheap crook and a merciless war criminal”, or “He speaks to the werewolf in us all.” You’d think that Bush would be just the person to get Thompson’s bile flowing, but, as many contributors to this film observe, by 9/11, Thompson was a spent force. It is, perhaps, Thompson’s awareness of his own diminished talent, that he could no longer make a difference, that drove him to suicide. “Hunter had lost his edge,” remarks one friend.

The decline is swiftly dealt with by Gibney, who instead focuses on Thompson’s incredible peak. So we get Thompson and the Hell’s Angels, Thompson running for sherrif in Aspen, the lysergic road trip to Las Vegas and, forming the centre piece of Gibney’s film, Thompson’s antics covering the ’72 Presidential campaign. From today’s perspective, it’s extraordinary to think that anyone, let alone someone as dissolute as Thompson, could get as close as he did to Richard Nixon and Democratic candidate George McGovern. One of the many high-ranking American politicians from that era who appear here, McGovern tells a story about having dinner with Thompson, who arrived at the restaurant and ordered three margueritas and six beers, for himself.

To give you some indication of Thompson’s influence, we get the story of how he all but brought down Democratic nominee Edmund Muskie by suggesting in a Rolling Stone piece that the senator was addicted to Ibogaine, a drug Thompson made up; a story that the press happily ran with. It makes Chris Morris and “cake” look like a rag week prank.

By the mid-Seventies, Thompson appeared less concerned with writing, more concerned with indulging himself in a rock star lifestyle. Covering the 1974 Ali-Fraser Rumble In The Jungle, he gave away his tickets to a drug dealer and spent one of the most important sporting events of all time lounging around in the hotel pool.

Gibney’s film attempts to try and find some motivation for Thompson’s behaviour. We find a man capable of warmth and kindness, as well as great bursts of anger. “He was aware of both, but not sure he knew how to control them,” says his second wife, Anita. Various talking heads – from Rolling Stone founder Jaan Wenner (resembling a particularly prosperous real estate developer) to author Tom Wolfe and Thompson’s conspirator, illustrator Ralph Steadman – add anecdote and personal insight. Along side the archive footage, Johnny Depp, sitting at a bar in what looks like Thompson’s office, reads from the author’s books and articles.

As a documentary, Gonzo is endlessly fascinating. Gibney, who was Oscar nominated for Enron: The Smartest Guys In The Room, marshals his extensive footage well, and despite a two hour running time, the film doesn’t drift. Partly, of course, that’s due to Thompson himself. Whether in his prime, discussing taking acid on the press corps plane in ’72, or later, his skin mottled and his speech slurring but still with a twinkle in his eye, he’s an extraordinary presence.

Gonzo will screen in this year’s London Film Festival, and gets a nationwide release in the UK on December 19