Rose Tremain’s autobiographical short story, inspired by an escapade from her own boarding school days, has been transformed into an extremely funny, charming and tremendously well-acted comedy written by Miriam Battye and directed by Molly Manners, all about sex, class, friendship and the awful encroachment of adulthood. As well as everything else, it refuses the glib happy ending of the traditional coming-of-age movie.

Newcomers Marni Duggan and Galaxie Clear give cracking performances as Flic and Minna, two year-10 girls and best friends for ever at a private school. They are not outsiders or emo losers; both are good at the brutal sport of lacrosse. Intent on raising their profile in advance of an attempt at Oxbridge, they audition for a production of A Midsummer Night’s Dream, which involves boys from a neighbouring school.

But they also capriciously decide that, like Titania and Bottom, they will “fall in love” with the first person they see after removing their blindfolds – this being unmarried geography teacher Miss Delavigne (Alice Englert), whom they wheedle into giving them “extra geography” at her private cabin on school grounds. The title, incidentally, also hints at a bold expansion of their own emotional territory. They are playing with fire.

This film supplies the laughs and the heartbreak and the insight that I blasphemously felt was missing from Alan Bennett’s The History Boys, although, like that oddly contrived film, this could just as well be happening 10 or 20 or even 40 years ago. The terrible injustice of that adult life for which they are so impatient is revealed to the two girls after the audition in which Minna was terrible and Flic was quite good; it is Minna who gets the lead, perhaps because of her specious blondeness, while Flic is given a humiliating non-speaking part, which compounds her unease at being a less well-off “scholarship” girl. As Minna looks like getting off with the insufferable boy playing Oberon, a terrible division begins to open between the girls.

Extra Geography recalls the wit and wisdom of Olivia Wilde’s Booksmart and Amy Heckerling’s Clueless, while Miss Delavigne’s New Zealand origins even brought back happy memories of Peter Jackson’s terrifying Heavenly Creatures. Flic and Minna’s friendship is based on a private language of their own, and you will have to acclimatise yourself to the stylised density of gags and zingers in the dialogue, which is worthy of Victoria Wood. When this secret world is contaminated by disloyal new alliances, it is very painful, especially for the person who feels left behind.

The movie leaves it up to us to decide if everything Flic and Minna do is just a diversion from the real thing: namely, their obvious feelings for each other. Or is it that their intense intimacy is immature and inauthentic, interesting only in that it is poignantly fated to evaporate when real grownup subjects are in play? Students of girl-power movies might sense another echo in the casting of Alice Englert; she starred with Elle Fanning in Sally Potter’s excellent Ginger & Rosa, which had a very similar dynamic. Extra Geography is an extra treat in the movie world’s school timetable.