Mirrors, make up and making out: that's pretty much everything the three cheerleading protagonists care about in the first act of Jack Heifner and David Kirshenbaum's musical. Beginning in 1963, Vanities: The Musical introduces us to Joanne, Mary and Kathy, who are such classic high-school airheads that when they are told, over the school tannoy, that the president has been shot, their immediate concern is whether the football game will still go ahead that night.

You've seen their like before - in films such as Clueless and Mean Girls - they are the popular, perfect ones. And these 16 year-old pre-college women, with their kneehigh socks and shorter than short skirts, are awfully blinkered. "I want the American dream," they sing at one point, not really understanding what that might actually be. And as they prepare for college, they reassure themselves that nothing will get in the way of them being best friends.

The first act of Vanities, is very funny but feels familiar: a dumb-kids extravaganza. But that's not quite all this musical is. When the plot jumps into the future, you begin to realise Kirshenbaum and Heifner are using these three muses to reflect on how lives change. We follow the women from school to sororities, to middle age and to later life. They grow right in front of our eyes, from empty-headed girls to women lost in an unfriendly complicated world.

In the story of these women, Vanities also parallels the changing face of America itself – from the innocent early '60s through to the '70s and beyond where presidents are shot, war is waged and drugs are taken with reckless abandon. It's not the most unique idea, neither is it delivered in the most original of forms. But it does what it sets out to do well and with comedy and pathos.

Racky Plews' excellent production has three superb performances at its heart. Onstage the entire time, Lauren Samuels (Mary), Ashleigh Gray (Kathy) and Lizzy Connolly (Joanne) are the leading light of this show. They are funny, silly, sad and real, and their performances bring layers - which just aren't there in the text - to their characters. Each one is nicely distinct - Samuels with her bored eyes and fake smile, Connolly with her home-girl obliviousness and Gray with her neurotic need to control. Their voices are uniformly great, dealing with the complicated songs beautifully. It is a joy to watch and hear them work together.

The songs themselves are pretty good. "I Don't Want to Miss a Thing" is an ear worm and though the rest of them aren't as catchy, they are well written, with lyrics that catch all the humour, the hope and the despair of the three women.

Plews puts the action on Andrew Riley's pastel-coloured set of shelves, where props and costumes are stored as the narrative moves on. The set becomes a little remembrance cupboard and it works for the tiny space at Trafalgar Studios. It crowns this bitter-sweet and surprising take on an everyman tale.

Vanities: The Musical runs at Trafalgar Studios until 1 October.

Watch the cast perform "I Don't Want to Miss a Thing"