Take Aunt Marge. The old bat pops in for a good groan, and an angry Harry inflates her like a Monty Python balloon. She floats off into the night sky and is last spotted clutching a smokestack near Sheffield. Uncle Vernon (Richard Griffiths) is increasingly wary of his weird, impulsive nephew. One more insult and Harry might splatter Vern over his brand-new conservatory like sandwich spread.

This is the reassuring prelude to Harry Potter and the Prisoner of Azkaban: the in-laws still hate him. The refreshing riposte is that Harry no longer gives a damn. Adolescence has bitten him, and it’s a sharp and pleasant surprise. Dangerous, too. Harry has discovered a taste for magic that verges on the reckless, and the Mexican director, Alfonso Cuarón (best known for Y Tu Mamá También), explores the urge brilliantly.

Cuarón’s appointment to this franchise is the most inspired Hollywood gamble of the year. He is not a proven director of blockbusters or indeed sequels, but any misgivings about his ability to bring home the lucrative bacon evaporate frame by lavish frame.

The change of mood and purpose is palpable. Hogwarts is a far richer and darker retreat than Chris Columbus’s gothic fairground. The portraits are more animated; the spooks more sardonic; the rivalries more poisonous. Yet the absurd humour of Michael Gambon’s headmaster, Dumbledore (a homage to Richard Harris) and Alan Rickman’s ever-marvellous Snape is a masterclass in oral joy. The atmosphere is that of an English Catholic public school, run by eccentric bachelors with a benign but questionable interest in the spiritual wellbeing of their pupils.

Harry, as ever, is the heroic source of pride and prejudice. A Prince William among wizards but a poodle to his peers, he is stalked by an escaped lunatic wizard, Sirius Black (Gary Oldman, who emerges far too late in the film), and haunted by soul-sucking wraiths. His first getaway, in a triple-decker London “knight bus” driven by a myopic nutter called Ernie (who gets his instructions from Lennie Henry’s shrunken head), is the most sublime piece of road-rage I’ ve seen.

But there are lovely shades of Sondheim about Harry’s adventures in the woods around Hogwarts. Hermione (Emma Watson) hides her hormones behind books, and Ron (Rupert Grint) cowers behind his inadequacies. But it is David Thewlis’s wonderfully smooth tutor, Professor Lupin, who unpicks the seam between the world of imagination and real adolescent anxieties in a film-stealing performance that uses nothing more sensational than words.

It’s this tension between friends and teachers that gives the film its gripping shape. The camera work is a sensual feast. Cuarón favours wide-angle lenses, and you could spend weeks drooling over the artwork in a single scene. If there’s a weakness to his film, it lies in the fiendishly ornate plot and the director’s blind faith in our ability to follow it.

The difficulty of distinguishing friend from foe is the film’s potent theme. But it becomes a maddening handicap when the story starts galloping around the final hairpin bends like a Hitchcock thriller.

The rare interest of this series is how the characters — and the films themselves — grow and mature before your eyes. I’m astonished how sensitively Cuarón filmed The Prisoner of Azkaban, and now I’m fascinated how Mike Newell will tackle the next.

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