An Education, Lone Scherfig, 100 mins, (12A)

Based on a memoir by Lynn Barber, An Education is about a 16-year-old girl in 1961 falling for a suave man in his thirties. Nick Hornby, who wrote the screenplay, has invoked Philip Larkin's pinpointing of the discovery of sex in 1963, "Between the end of the Chatterley ban/And The Beatles' first LP".

But what makes An Education so precise a period piece is that it is set in the twilight of the era of the Romantic Older Man, for it was he – the "Mr Rochester type", as he's referred to here – that the Beatles would make obsolete. As we watch Jenny (Carey Mulligan) swoon over her raincoated admirer David (Peter Sarsgaard), her very attraction to him seems the period element, while she coolly snubs her earnest schoolmate Graham (Matthew Beard). Two years later, the likes of Graham would be donning Cuban heels and seeing off gabardined older rivals with a flip of a Ringo fringe.

But this is still 1961, and An Education makes the adult world – at least, its more European aspects – seem jolly dashing. Weary of her Twickenham adolescence, Jenny is earmarked for a place in Oxford, but hankers for French sophistication, swooning to Juliette Greco songs under mock-Tudor eaves. Then David drives up, charming her with small talk about Elgar. He soon has her hooked with the high life: a Ravel concert, a Pre-Raphaelite auction and a visit to a Cambridge pub, where David forges C S Lewis's signature. As all this suggests, An Education conjures up a world of tweedy saloon-bar glamour, still of the 1950s, as chronicled by Kingsley Amis and early Muriel Spark. To today's eyes, the idea of a teenage girl bedazzled by such genteel fustiness is so fascinatingly incongruous that it's a shame for the film to overstate its case by also pandering to our idea of period cool, in a nightclub scene complete with a sultry chanteuse.

Otherwise, the film rings very true, especially in capturing its social bestiary: Jenny's Pooterish suburban parents (Cara Seymour, Alfred Molina); her crisp bluestocking mentor (Olivia Williams); David's pals, a gilded young couple of mondains (Dominic Cooper, Rosamund Pike, the latter show-stoppingly funny as a militantly thick glamourpuss).

In fact, Molina steals the film as the paterfamilias riddled with the prejudices of his time: a relishable moment has him blustering his way out of an anti-Semitic remark in front of David, who's Jewish. He's not a hateful man, but it's quietly shocking to see how his petty vanity makes him complicit in his daughter's seduction.

The director, Lone Scherfig, is an alumna of the Dogme approach, but here her touch is polished and rather impersonal. The script offers moments of discomfort for which Scherfig isn't quite up to twisting the knife. She could have made more of the bedroom scene in which David breaks the erotic spell by calling for baby talk – which, of course, Jenny is far too sophisticated to indulge.

Altogether, Jenny seems too classy for this seedy suitor, a relative of the Beatles' "man from the motor trade". I'm not sure I entirely buy Sarsgaard as Jenny's heart's delight, with his smooth-jowled blandness and oddly squeaky voice. But perhaps it works to the film's advantage that David is clearly not the real thing: a smart move, then, to cast an American as a quintessentially bogus Englishman.

As for the smokey-voiced Carey Mulligan, she is undoubtedly the British find we've been reading about – wry, radiant, pertly oddball in looks – but the film puts her too much in pride of place on its mantelpiece. The editing could have omitted a few of those throaty chuckles, while the photography never misses a chance to highlight the ironic dimple by her mouth: Mulligan is barely given a moment's break from charming us into falling for her.

And her Jenny is slightly too good to be true: a projection of the savvy girl who will soon look back at love's valuable lessons, rather than the girl learning them in the here and now. The film's one big mistake is her showdown with Emma Thompson's tautly forbidding headmistress. When Jenny weighs in with her piece in the central debate about the value of learning, it's that bit too clarion and finely written, too neatly what a 2009 audience wants to hear a smart, rebellious young woman saying about the values of the benighted past.

Still, while the package is all wrapped up a little too neatly, there's no denying the classiness and wit of its contents. An Education is intelligent and hugely enjoyable, even if, as a knowing exercise in cultural hindsight, it's not quite the British Mad Men.