Growing up is hard to do, as countless coming-of-age movies have shown, some more affectingly than others.

With “Ginger & Rosa,” British avant-garde filmmaker Sally Potter (“Orlando”), offers up a strong entry into the field with what is by far her most appealingly mainstream film to date.

An intimate character study, “Ginger & Rosa” is set in England in 1962. It’s told mainly from the viewpoint of Ginger (Elle Fanning), a 16-year old budding poet growing up in post-WWII England alongside her best friend, Rosa (Alice Englert, the daughter of director Jane Campion). The two were born on the same day, in the same hospital, and have been BFFs ever since.

Now, though, they’re 16 and their paths are beginning to diverge. Ginger is hyper-aware of growing up in the shadow of the mushroom cloud. She constantly frets over the possibility of imminent, worldwide nuclear destruction; she joins the Ban the Bomb movement and marches for disarmament. Rosa marches alongside Ginger at first, but her interests are fast heading towards boys, mascara and smoking. She is adopting a live-for-today philosophy.

The two reach a seemingly unbridgeable divide when Rosa becomes romantically involved with Ginger’s father (Alessandro Nivola), a pacifist and academic. He has always lived outside of society’s rules and it seems a no-brainer to him that his love life should follow suit.

“Ginger & Rosa” has several things going for it, most notably an achingly intense performance from Fanning, who was 13 when the movie was shot. She nails, in the most naturalistic way possible, the acute feelings and emotional whiplash that are the daily, nay, minute-to-minute reality of adolescence.

In the slightly smaller role of Rosa, newcomer Englert is equally effective. From the lost look in her black, heavily eyeliner-etched eyes, it’s clear that her fatherless Rosa -- the girl’s dad walked out when she was small -- is going to seek masculine affection and answers where ever she can.

Potter, who both wrote and directed the film, surrounds her adolescent protagonist with a handful of adults, some of whom are more helpful to Ginger than others. These include her mother (“Mad Men’s” Christina Hendricks, in a strong turn), her father (Nivola, in an marvelously ambivalent performance), her seemingly gay godfathers (Timothy Spall and Oliver Platt, an amusingly improbable pairing) and an American feminist poet friend (Annette Bening, who makes the most of her few scenes).

“Ginger & Rosa” offers a nuanced portrait of a girl uneasily on the verge. Adolescence is always scary; Ginger’s apprehension about the future -- the Cuban missile crisis occurs near the end of the movie -- makes hers even scarier, at least to her.

In one scene, after she vehemently expresses her anxiety over everyone getting nuked, one of her godfathers pleads, “Can’t you be a girl for a moment or two longer?”

It’s a marker of the film’s success that we wish the same for her even as we know that she’s indeed going to grow up and get past all this. If we’re lucky, we all do.