Sex & Drugs & Rock & Roll, Mat Whitecross, 115 mins, (15)

Andy Serkis reveals many layers of Ian Dury's character in this compelling biopic of the late Blockheads frontman

My favourite ever bit of on-stage repartee was from the late Ian Dury, addressing a punter in the front rows. "I like your shirt." Pause. "But I don't like you."

It's routinely said of the singer and wordsmith that he belonged as much to music hall as to rock'n'roll, and that's true: he built a bridge between George Clinton and Gene Vincent on one side of the pond, Max Wall and Noël Coward on the other. And the way Dury used his disability – he contracted polio as a child – to parody and subvert the traditional physical show-offery of the rock singer made him a performance artist par excellence. Once, at the 100 Club in London, he made the most startling entrance I've ever seen, ploughing through the audience with his walking stick before being heaved bodily on stage by a roadie.

Sex & Drugs & Rock & Roll, directed by Mat Whitecross and written by Paul Viragh, reminds us that Dury was a more complex figure than the raucous geezer persona that made him a mainstream star. He was a product of the British art school world and a denizen of London's 1960s-70s jazz-art bohemia. That is at least sketchily established in a messy but buoyant biopic that celebrates its subject without quite capturing the essence of his brilliance and strangeness.

The film is a patchwork of dramatic episodes, Fellini-esque on-stage narration by Andy Serkis as Dury and eye-singeing Peter Blake animations. We see Dury as the struggling leader of Kilburn and the High Roads, a band of misfits too outré to make any commercial inroads. Against all likelihood of success, he's dedicated to his art, somewhat at the expense of his loved ones. The film would have us believe that while first wife, Betty (Olivia Williams), was in labour in their two-up-two-down, Dury was rehearsing the band downstairs. In she walks, red-faced: "I've just given birth. Any chance you can keep the noise down?" (Take this with a pinch of salt: as Dury remarks, "Never let the truth get in the way of a good story.")

In this story of rag(amuffin)s to riches, Dury swaps the love of one good woman for that of another (Naomie Harris), finds a co-writer (Chas Jankel, played by Tom Hughes) who can knock out a hit tune, and becomes a star. But sudden fame proves sour for a man long used to obscurity. "Touch me!" cries a fan. "I'm not the fucking Pope, am I?" Dury retorts. Soon he's encamped with his entourage at a country estate, and indulging in studio outbursts.

Flashbacks delve back to the sources of Dury's defiant and abrasive spirit: his sojourn in a children's home of Dickensian harshness, with Toby Jones as a Squeers-like supervisor. It wouldn't be a biopic without some parental woe: Dury's chauffeur father appears in hazy reminiscences, a hulking hero (Ray Winstone, who else) who teaches young Ian to fight for himself. But the film is most acute when addressing Dury's own fatherly shortcomings towards son Baxter (Bill Milner), the tyke seen lounging on the cover of the New Boots and Panties!! album. As Dury's career takes off, the film increasingly, and compellingly, becomes the story of Baxter, whose problems begin when Dad entrusts him to the care of fearsome minder the Sulphate Strangler (Ralph Ineson), who tends to leave his pills lying around, accessible to all.

Young Milner's affecting performance helps to make Sex & Drugs more insightful about the drawbacks of having famous parents than about fame itself, or indeed about Dury. There's much about what made the man psychologically, not enough about what made him culturally: we might have had a glimpse of the art school years, and more of the hipster underground sketched in one party scene. Dury puts it nicely, though, when Baxter anxiously asks if their family is posh: "No," replies Dad, "we're Arts and Crafts."

Mat Whitecross co-directed The Road to Guantanamo with Michael Winterbottom, and it is Winterbottom's pop-historical 24 Hour Party People that Sex & Drugs ... most resembles formally. The presentation as Dury's autobiographical stage show forms a loose structure for a scrappy, breathless narrative. The self-conscious lantern-lecture aspect just about offsets the psychological patchiness and occasional obviousness. (Here's another biopic in which, when fame messes up the hero, his girlfriend ruefully announces, "I don't know who you are any more.")

Otherwise, Sex & Drugs ... stands up pretty well as a celebration of Dury: this is film as tribute act. Andy Serkis catches the manner to a T, uncannily pinning down the nuances of Dury's stylised facial language, the comic tics and eye-rolls. Serkis performs the songs, accompanied by Dury's old band the Blockheads, and he does it with gusto and precision, getting both the costermonger roar and the sly, coy lounge-singer inflections.

Serkis's face, however, is so distinctive in its hobgoblin spikiness that there's barely a scene in which the actor doesn't come across as considerably more perverse and menacing than Dury himself: Serkis is more Fagin to the singer's Bill Sikes.

Even so, it is a gale-force turn that gives the film the charge that it needs. While it feels slapdash rather than properly punk-collage ragged, Sex & Drugs & Rock & Roll is an honest job, and it makes a good case for including Dury's work and personality in any Brit-culture list of Reasons to be Cheerful.