Once upon a time there was a director called Tim Burton who made a perfect film. You probably haven't heard of it. It was called Vincent, it was six minutes long and its wild-haired hero was an inventor of horrors, fascinated by the dense London fog.

Since then, Burton has made lots of films, most of which (Batman, Beetlejuice, Edward Scissorhands, Planet of the Apes, Charlie and the Chocolate Factory) you'll know very well indeed. None of them is flawless - what they possess are great bits. Which is why it's such a pleasure to report that with his new offering Burton has come full circle with a wild-haired hero who gets up to all sorts of wicked things in old London town, in the just about perfect Sweeney Todd.

An adaptation of Stephen Sondheim's award-winning musical, this blood-soaked spectacular is 110 minutes long, but hurtles along with such momentum that it's over in the blink of an eye.

It starts on board a ship, with working-class barber Benjamin Barker (Johnny Depp) - now re-christened Todd - explaining how he was robbed of his wife and daughter by a lecherous judge (Alan Rickman's Judge Turpin) and packed off to the colonies.

Fifteen years later Todd is back in Fleet Street and set on revenge. Having recovered his trusty silver blades, he plots to get his hands on the judge. However, thanks to a string of bad luck, he is forced to go on a killing spree instead, slicing the throat of anyone who sits in his barber's chair then, at the pull of a lever, dropping the body down to the basement.

His neighbour, Mrs Lovett (Helena Bonham Carter), eggs him on. She has realised that human remains are just what her tasteless pies have been lacking.

Business booms and Lovett dreams that she and Todd will one day settle down and raise a young orphan called Toby (Ed Sanders). But Sweeney has a one-track mind: all he wants is Turpin.

Sondheim purists be warned: Burton and screenwriter John Logan have boiled down the brilliant, but undeniably panoramic, Broadway show. There are fewer songs, fewer characters and no chorus observing things from on high, which creates a wonderfully oppressive atmosphere.

The demented orchestral manoeuvres beat us around the head; the chilling, childish melodies tiptoe under our skin and refuse to leave. We are in an artificial world - a fever-dream of industrial London, full of phoney cobblestones and even phonier cockneys. Depp looks like Cruella de Vil's morose cousin; Bonham Carter is a cross between a sex doll and Madame Guillotine.

The colourful, Brechtian libretto ("There's a hole in the world like a great big pit and it's filled with people who are filled with shit!") only adds to our estrangement from solid ground.

In this heightened state, it's hard not to connect with the killer and his accomplice. Thanks to increasingly intense performances from Depp and Bonham Carter, it becomes impossible. Todd is an immovable man who moves us, Mrs Lovett a treacherous entrepreneur whose sloppy need for love makes us weep.

It may actually help that the (untrained) Depp and Carter have merely adequate voices. The sense of this couple's vulnerability is overwhelming.

As for Burton, he seems both energised by Sondheim's material and chastened, as demonstrated by his treatment of Sacha Baron Cohen's Pirelli.

Todd's rival barber, a preening fop, he provides the film with its most obvious laughs. His accent (and the codpiece that bulges from his tight blue trousers) is stupendously funny but Cohen is kept on a tight leash: just as he starts to steal the scene, it ends. Burton's previous films were prepared to drop everything for a cool gag or a big-name turn. Not any more. Here, he's a man on a mission.

It transpires that two betrayed children lie at the heart of this tale. There's Toby, the adoring urchin Mrs Lovett promises to protect in the film's most memorable duet ("Nothing's gonna hurt you, not while I'm around!").

There's also Sweeney's long-lost daughter, Johanna (Jayne Wisner), whom Turpin keeps locked up in his fortress-like home and later slings into an asylum. At first glance, the voluptuous, elfin-faced Johanna looks like every other bland blonde in Burton's oeuvre (epitomised by Christina Ricci in The Legend of Sleepy Hollow).

Yet through her we understand the horror - the insanity - of being defined solely in terms of pretty yellow hair. Neither the judge nor society at large give Johanna room to breathe. The seismic shock is that Sweeney is equally willing to see her entombed.

Tim Burton says that, as a child, he felt "buried alive" by his parents' values, that he dreamed of "venting anger - on a grand scale". Here, set free by Sondheim, he lets rip, fusing the personal and the political into a blazing whole. Sweeney Todd is about the rancid, death-dealing class system.

It's about legal corruption and (very topical, this) the corners cut by unscrupulous purveyors of fast food. We are what we eat. But it's also an intimate, savage study of parenting.

Depp deserves his Oscar nomination but it's no surprise that the film itself is not in the running. Happy endings aren't what this killer fairytale is about.