They say that inside every great comic, there’s a miserable git sulking in the corner of the self. But funny man Peter Sellers was more of a Hyde than a Hamlet. For inside this much-loved clown, there lurked a monstrous brat waiting to escape and rampage through the lives of loved ones. And, as the director Stephen Hopkins’s film makes clear, it often did.

Why make a film about the life of Peter Sellers, anyway? True, he had four wives, eight heart attacks and 60 films to his credit, and he slept with the 18-year-old Britt Ekland. But a life that sounds good on paper doesn’t necessarily work on the big screen. As Sellers once said: “To see me as a person on screen would be one of the dullest experiences you could ever wish to experience.” This isn’t a dull film, but unless you’re a serious Sellers fan, it’s hard to see what’s so interesting about his story.

The film begins in the late 1950s. A podgy Sellers (Geoffrey Rush) is a frustrated star of radio — The Goon Show — who wants to break into films. Wrong face, says one cruel casting agent (Alison Steadman). With a push from his mother, Peg (Miriam Margolyes), Sellers perseveres and first makes his name as the young thug in The Ladykillers. As his career progresses, so his life falls to pieces.

Sellers’s unrequited love for Sophia Loren (Sonia Aquino), with whom he starred in The Millionairess, leads to the break-up of his marriage to his long-suffering wife, Anne (Emily Watson). London starts to swing, and so does a new and slimmed-down Sellers. Success has clearly gone to his penis: he paws every dolly bird in sight as the soundtrack blares out What’s New Pussycat?. Then he marries Britt Ekland — played here with a wonderful luminosity by Charlize Theron — and has a heart attack. When Sellers takes the supporting role of Inspector Clouseau in The Pink Panther, in 1963, he becomes an international star.

The screenplay avoids making a causal link between Sellers becoming a big star and becoming a big shit. He’s shown not as a victim of celebrity, but of something equally lethal: a monstrous mum. Peg, nicely underplayed by Margolyes, is a ball-busting wife and pushy stage mother. When the dispirited Peter is thinking of giving up on films, Peg says to him: “Want to be a failure like your father?” Hopkins (Lost in Space, 24) has no background in comedy, and it clearly shows. If you’re going to make a film about a “comic genius”, you have to show his genius in action. We get dozens of Sellers’s best-loved characters (Dr Strangelove and Inspector Clouseau), but very few laughs. If you know the sketches, you can giggle along, but if you’ve never seen a Peter Sellers film, you might wonder what all the fuss is about.

The film portrays Sellers as a tortured genius whose tragedy is summed up by the man himself when he says: “There is no me. I do not exist. There used to be a me, but I had it surgically removed.” The idea is that he was nothing more than the sum of his various parts. Actually, he wasn’t a tortured genius — he was a genius who tortured other people. And as for the idea that he had no “me” — well, Sellers did have one. It was just a petty, insecure, spoilt, violent, malicious, bullying and bratty “me”.

The film is at its dramatic best when portraying this side of Sellers. He would throw unbelievable tantrums towards his wife, his directors and, worst of all, his children. There’s one brilliant and chilling moment when Sellers, who is planning to leave his family for Loren, is asked by his little girl: “Do you still love us, Daddy?” Sellers crouches down as if to comfort her, and softly says: “Of course I do.” He pauses and then adds: “But not as much as Sophia Loren.”

In terms of chronology, the film follows the conventional rise-and-fall structure of the traditional biopic. But this is a biopic that is desperate not to appear to be an old-fashioned biopic. So Hopkins has tried every trick and gimmick imaginable to cover his tracks. Not only do characters speak directly to camera — which, outside of Michael Caine in Alfie, never works — we see the making of the film we’re actually watching. And we have Geoffrey Rush playing Sellers, who is in costume playing various people in his life.

Hopkins has explained this curious method thus: “We have approached the story as a film by Peter Sellers about Peter Sellers... making a film of his own life the way he wanted it to be.” But hold on, Sellers wouldn’t have made a film out of his life. As he said, it would be too dull. As a result of this unconventional approach, what we end up with is a film with dozens of Peter’s voices, but without a voice of its own.

Watching Geoffrey Rush in Shine, it never occurred to you that he wasn’t the pianist David Helfgott; watching him here, we’re never allowed to believe that he’s Peter Sellers. At times, Hopkins’s film is like a manic episode of Stars in Their Eyes: “Tonight, Matthew, I’m going to be Stanley Kubrick, Peter’s mum, Blake Edwards...” In the end, it’s just a bravura display, not of acting but of mimicry.

The Life and Death of Peter Sellers, 15, 127 mins, two stars