Radio DJ, former TV chat show host, Norwich ambassador, grammar pedant and militaria enthusiast Alan Partridge has been with us for so long - over 20 years, now - he feels like a fixture, part of the comedy furniture. We've followed his career and his personal life through ups and downs (more downs than ups), from short-lived TV stardom to the graveyard slot on local radio, from divorce and depression to, as the autobiography puts it, Bouncing Back. Like his long suffering PA Lynn (Felicity Montagu), we've lived with Alan through his best and worst.

Alan's fictional career on TV was short-lived, and he's been back on local radio ever since Knowing Me, Knowing You was cancelled by the BBC after he punched a wheelchair user and the boss of comedy on live TV during the Christmas special. Of course, his meta-career has followed the conventionally successful trajectory from radio to TV, and the next logical step, a Partridge film, has been in the pipeline for years. But did we really need a feature-length dose of Alan? Can we stomach seeing that face twelve feet high on the big screen? And could his signature brand of comedy of embarrassment and obsession with the minutiae of small-town English mundanity retain any resonance in 2013? In short, is Partridge still funny?

Thankfully, the answer to all these questions is yes. Alan Partridge: Alpha Papa is hilarious. From its opening moments, the film lets you know you're in safe comedic hands. The visual and musical gags begin before the idents are even over. The production design is wonderful - Alan's world is portrayed immaculately, down to the last corporate mug. Everywhere you look there's another sly little joke. The script lives up to the setting, too. No opportunity to poke fun at dismal British holidays or supermarket self-checkouts is lost. For once, the trailer doesn't reveal the best gags, and it would be a crime to do so here. It's really tempting, though, because many of the jokes are truly excellent, building upon the foundation created by the setting and story with razor-sharp writing and beautifully executed slapstick.

Alan is currently working as a DJ at North Norfolk Digital radio, hosting phone-ins on topics like taxi drivers and soup flavours, spinning soft rock anthems and providing quality banter with his sidekick Simon (Tim Key). But change is coming: a huge media conglomerate called Shape has bought the station, and its heartless executives want to modernise the content and get rid of dead weight. The station boasts an array of talent for them to choose from, but they narrow it down to Alan or his colleague, hapless late-night presenter Pat Farrell (Colm Meaney). Alan cravenly stabs Pat in the back, of course, little suspecting that his sacking is going to prove to be the last straw that breaks poor Pat's mental stability. The next thing he knows, Shape's takeover party is ending in a siege, with Pat holding station staff and Shape executives hostage at gunpoint, and insisting he'll only talk to the police through Alan. Alan's immediately propelled into every action film he's seen, racing through corridors and wisecracking to the police - in his mind, at any rate. The reality is an amplification of his usual mixture of verbal diarrhoea and social inappropriateness.

Alan's lurching from panic to pride to self-serving cunning as he reacts to his situation is a masterclass in comic acting from Coogan, who has boiled Alan down to perfection over the last two decades. He's refined all the gross extremes of his character into a perfectly nuanced portrait like a chef blending strong spices into a richly balanced curry.

Alan would be nothing if he wasn't a product of his environment. He's East Anglia's first son. Never mind the writings of WG Sebald, Norfolk has Alan Partridge. The mysterious fens are just an indistinct backdrop, the countryside a place to tow your speedboat through. Alan's milieu is the new-build cul-de-sac, the motorway service station, the chain hotel conference room. It's well-established satirical territory, the depressingly aspirational small-town preoccupations of the English lower-middle-classes, the Daily Mail level petty snobbery and crass bigotries.

It's easy enough pickings, of course - Partridge vehicles have been skewering this stuff since I'm Alan Partridge switched the spotlight onto Alan's personal life. Like all satire, Partridge wouldn't work if it was only one-dimensional. There has to be a core of meaning at the heart of it, something that goes beyond the bathos to illuminate some kind of wider and deeper truths. The disgusting medical conditions, the casual racism, the cringe-inducing efforts at talking to women - they're funny, but they'd be crass without the layer of insight that Coogan gives Alan. On some level, he knows what the right thing to do would be; he sees through the absurdity of the stereotypes around him and he's as aware of what's going on as we are. Every so often he says something perceptive, something that reminds you that you're in this with Alan; Coogan's genius is to make this another layer of the comedy, something that deepens it rather than sitting smugly on the surface.

The rest of the cast are uniformly great, too. Familiar characters like Lynn and ex-soldier Michael (Simon Greenall) are joined by an array of larger-than-life caricatures - psychotic policemen, awful breakfast DJs, crazy drunk women, bastard paparazzi, boring ex-junkies. Whilst they're often one-dimensional, it doesn't matter - all the central conflicts are Alan's, the supporting characters foils for his unstoppable ego. Alan's the star, just as he is in his own head, whether or not this is the story of someone else's breakdown for once.

Alan Partridge: Alpha Papa has elevated its source material to the big screen beautifully. A bit like The Inbetweeners (Ben Palmer, 2011), it proves that its characters are strong enough to deliver comedy on a much more ambitious scale. Director Declan Lowney and writers Steve Coogan, Armando Iannucci, Peter Baynham, Neil Gibbons, and Rob Gibbons have managed to execute a film that could have faced so many pitfalls with consummate ease. They make it look simple, when it's anything but.