The Beatles didn’t just come from Liverpool, they were made here. The tang of the city flavours their songs. Their blend of absurdity, wry wit, cocky assurance and warm compassion is, perhaps, most succinctly sampled in the 13 tracks of the band’s eighth album, Sgt Pepper’s Lonely Hearts Club Band. To celebrate the 50th anniversary of its recording, Liverpool decided to stage a three-week festival across the city: 13 events, each based on a track from the album. Which is how Phelim McDermott of Improbable theatre company and 20 Stories High – the decade-old company that creates theatre in collaboration with young Liverpudlians and world-class professionals – found themselves workshopping ideas around She’s Leaving Home. I confess that I imagined I’d be able to anticipate their conclusion (the song is, after all, a staple of youth drama improvisations). I was so wrong.

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Their creation prises open cracks in the ordinary. We, the audience, gather in the sitting room of a private home. Kelsey comes in, a girl in school uniform, who performs household tasks and talks, partly to herself, partly to us, admitting us into her life. She leaves; returns. Years pass between entrances and exits. In the interludes, yellow-frocked, duster-wielding puppeteer Zoe Hunter surprises us with miniature scenes, created from odds and ends: Kelsey’s baby brother’s toys, a cereal packet, a bobbin of thread. These circus-inspired numbers imaginatively transpose Kelsey’s situation (witty takes on a caged tiger, a high-wire act). In a corner under a TV set, a cellist with pink epaulettes shades the moods (Semay Wu also composes music and sound effects).

The terraced house in which we sit transforms into a magical realist world, sensitively realised under Julia Samuels’s direction. Keith Saha’s script catches the cadences of teenage speech, flecked with poetry – excited at the prospect of a party, Kelsey is “pissing glitter”. Brodie Arthur as Kelsey delivers a performance of extraordinary breadth, depth and sensitivity. The setting beautifully amplifies the intimacy of our immersion in this life, but this production would succeed equally in other spaces. It certainly deserves a life beyond the festival.