It's only at the end of Fish Tank that we discover the name of the heroine's dog: Tennent's.

I'm glad writer-director Andrea Arnold kept this detail quiet; if she had revealed it early on, Fish Tank might have come across as a broad-stroke essay in chav anthropology. As it is, there's little in the film that doesn't ring true: Fish Tank is as convincing a picture of life on the Essex estates as Arnold's debut Red Road was of a similar Scottish milieu.

If Fish Tank isn't quite as good as its predecessor, it's only because Red Road's eerie existential-thriller aspect made it a distinct anomaly in British film. Altogether more familiar, Fish Tank could almost be considered an archetype of Brit realism, of scuffed school-of-Loach working-class drama. It's a vein of cinema in need of reinvention, and Arnold may not rethink it from the very roots in Fish Tank, but she carries the film off with fresh, abrasive clarity.

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Fish Tank is set in a bleak stretch of Essex, near Tilbury, where even the roadside vegetation has a wizened, skanky look. The protagonist is 15-year-old Mia (Katie Jarvis), the kind of girl who's more usually a statistic than a person who art-film audiences get to know in any depth.

She's the scowling hoodie on the corner, an embodiment of the tabloids' "broken Britain". We think we have her measure at the start when Mia strides angrily towards a gang of her peers practising a sullen girl-group dance routine, and head-butts one of them. Then she slopes off back to the council flat where her mother Joanne (Kierston Wareing) – more like a foul-tempered, abusive big sister – spits invective at her. It's a horrible, sour, piss-off world that Arnold paints.

Officially a social problem, Mia is destined for a pupil referral unit where she will be off her mother's hands. A loner, Mia is only at ease in an abandoned flat practising solo dance moves. Framing the film in a cramped, nearly square ratio, Arnold and director of photography Robbie Ryan evoke the claustrophobia of Mia's world, show how her natural energies are boxed in, urging to burst as she dances with angry, muscular intensity.

One day, a stranger walks into Mia's kitchen: a bantering Irishman called Connor (Michael Fassbender), who is Joanne's new boyfriend. Despite Mia's initial defiant unease, something thaws around her. Connor mellows Joanne with attentive charm and vigorous sex, takes the family out to the country, and introduces Mia to his favourite music ("weird shit", Joanne calls it, though it's nothing more outré than "California Dreamin'"). Despite this upturn in Mia's life, we're not fooled: from the first appearance of Fassbender's bare-chested, wolfishly charismatic Connor, we see where things are likely to go.

In its last stretch, the film takes a different direction, towards the kind of soul-wrenching crisis that tends to climax the Dardenne brothers' films. Arnold gives us a genuinely nerve-wracking sequence on the Essex marshes, but at the last moment, pulls back from the horror that seems inevitable. That's merciful, and in keeping with the film's overall tone, but I'm not sure Fish Tank needed to go out to that edge in the first place.

In fact, the film is at its best when simply evoking the day-to-day tawdriness and boredom of Mia's life. Arnold maps her heroine's world with an acute sociological eye, especially when showing how a knowing but still vulnerable teenager is callously excluded from the domain of adulthood. No longer a child, Mia is kept well away from her mother's parties, where adults gather in the kitchen to fumble sweatily in each other's knickers: her mother's sexual rivalry towards Mia is neatly pinpointed, and Kierston Wareing is superbly abrasive as the slutty, seen-it-all Joanne.

Sometimes Arnold tries a little too hard to muster a more portentous dramatic resonance: Mia is fascinated by, and tries to free, a scrawny horse chained in a yard, a creature that looks far too fragile to support the weight of symbolism piled on its ragged bones. The film ends touchingly on a near-wordless rapprochement, a bitterly unsentimental moment of casual intimacy, as Joanne and her two daughters dance to a rap telling us that life's a bitch and then you die. Alas, Arnold all but disperses the power of this scene by ending the film on a crunchingly obvious "poetic" skyline shot.

The film has a terrific lead in new name Katie Jarvis, famously discovered having an argument with her boyfriend. She's immensely affecting as Mia, never a cartoon of defiant feistiness, but a complex mix of determination, fragility and sandpaper cussedness. Also good is another newcomer Rebecca Griffiths, as Mia's kid sister, Tyler. Uneven as it is, Fish Tank is a powerful film from a director with a steely take on the world, who is able to make Essex look almost soulful.