Give Judi Dench half a chance, and she'll make a lot more of a good part than almost any other actress. That, perhaps, is a well-established given. But in Richard Eyre's very British Notes On A Scandal, which premiered in New York last night, she excels herself.

There isn't a false note in her riveting performance as Barbara, an old maid school teacher, lonely and frustrated, but the only one who can keep discipline in a decaying London secondary school where even the most recalcitrant pupils daren't cross her.

Taken from Zoe Heller's Booker Prize-nominated novel, the film looks at her through a magnifying glass throughout as she plots to gain the friendship of Sheba, Cate Blanchett's new and naïve art teacher, and finds a convenient way of binding her to her possibly lesbian bosom.

The young teacher allows herself to be trapped when the older woman finds out she has allowed herself to have an affair with a handsome but needy young pupil (Andrew Simpson). Only Barbara discovers the secret and, while professing a shocked sympathy, threatens to expose it when the affair continues despite Sheba's promise to call it off.

The outcome, Barbara hopes, will cleave Sheba ever more tightly to her. But it doesn't, and can't, work out that way. Patrick Marber's excellent screenplay and Eyre's sensitive direction sum up school life with a few deft strokes before launching into the deadly drama of the boy's obsession for his teacher and the even deadlier fixation of Barbara for Sheba, whose marriage-to an older man (Bill Nighy) is on the rocks.

Besides Dame Judi, there are three other fine performances which render the film as watchable as it is. Blanchett's shows just how the young woman traps herself in the emotional loop of a hopeless affair, Nighy is as convincing as ever as her kindly unsuspecting husband who finally explodes with pent-up fury, and Simpson's enamoured pupil beautifully sketches in the turmoil of youthful emotions that can only lead to something like tragedy.

But it is Dench who dominates the film, lending it power and veracity, even if the final sequences may seem overly melodramatic to some. Watch the sequence when she has taken her dying cat to the vet and demands that a harried Sheba go with her as her only real friend, and you will see a microcosm of what the film is about. It concerns loneliness and despair. As Barbara says: " People have always trusted me with their secrets. But who do I trust with mine?"

• Notes On A Scandal opens in London on 2 February