At first this Broadway musical about a teenage girl with a fatal ageing disorder – yes, you read that right – threatens to be the height of mawkishness. But there’s a darkly witty, astringent core to David Lindsay-Abaire’s book and lyrics and a subversive zest to Jeanine Tesori’s music. Michael Longhurst’s wry, nimble production also hands 66-year-old musical theatre star Maria Friedman a glittering singing role and an acting challenge she mostly navigates with aplomb. It’s great fun.

At heart, Kimberly Akimbo is an acerbic take on the tropes of US high school drama. We’re in Bergen County, New Jersey, where sundry nerdy and sexually confused kids on the brink of adulthood congregate at the local ice rink, the only local entertainment. Each is locked in a private hot shame of adolescence but Kimberly Levaco’s (Friedman) is different.

A rare genetic inheritance, progeria, means she ages four to five times faster than her peers and is unlikely to survive far beyond her imminent 16th birthday. Her parents had her accidentally and young, and the burden their shared biology has inflicted on her breeds chaos in the family: her dad’s a feckless drunk, her mom’s a needy hypochondriac, and chancily pregnant again.

There’s also a rogue, sociopathic aunt Debra (Alice Fearn, in a turn that would be a show-stealer if Friedman and Gilli Jones as the young male lead Seth weren’t so strong). Kimberly’s classmates seem generally accepting but it falls to her to cover their gaucheries around her condition. On every front, she’s compelled to be older than her years.

The plot, such as it is, concerns a check-fraud plan by Debra that will cover a wished-for, unifying family road trip and costumes for the class choir at a singing competition. But really we’re here to witness the sweet and sometimes surprising ways Kimberly’s situation impacts on her family and peers. A softer side to her parents is revealed in the video messages they record for her unborn sister, projected onto the walls of Soutra Gilmour’s rotating, doll’s house set.

The four teenage show-choir members – all pining futilely for one other – are amusingly sketched in. But it’s Kimberly’s tentative friendship with Seth - a motherless, tuba-playing dork, obsessed with anagrams and The Lord of the Rings – that really blossoms.

This part could very easily tip into schmaltz or ickiness, particularly when matters seem set to turn romantic. But Gilli Jones brings a pure, sunny-faced innocence to Seth, as well as a strong, clear voice to his rueful ballad Good Kid. Which, incidentally, also features a winning tuba solo.

The score kicks off with the sassy establishing ensemble number Skater Planet and the staccato speech-songs Hello, Darling and Make a Wish. Then it flowers with the rich group numbers Anagram and Better, and the hopeful first-act closer This Time. Kimberly gets few solos but her lead parts in the group numbers, and the delicate duet with Seth, Now, showcase Friedman’s ability to freight music with feeling. She stands out amid a cast that’s in uniformly fine voice.

The show is based on Lindsay-Abaire’s 2001 play of the same name and grew out of his and Tesori’s wish to collaborate on something more intimate after they worked on Shrek the Musical. Kimberly Akimbo won several awards off-Broadway then five Tonys when it transferred, and you can see why. On one level it’s a crowd-pleasing, smart-aleck riff on familiar tropes of American popular culture: the high school, the small town, the blue-collar family that can’t articulate affection.

On another it is hugely challenging. This is a cheery musical about inevitable death. Not once but twice it sadistically requires the cast to caper around the stage on ice skates. And it asks an older actress to play a young but preternaturally wise spirit in a prematurely old body. If there’s a flaw in Friedman’s performance, it’s that she never quite captures Kimberly’s youth. Never mind. After a long drought, Hampstead has a hit.

To 7 Nov, hampsteadtheatre.com