“The backbeat of a snare drum, set against a four-square, driving rhythm, was the early hallmark of rock ’n’ roll,” the programme helpfully informs us. The show itself, first seen last year at the Glasgow Citizens, is an exhilarating account of the Beatles – then known as The Quarrymen – in Hamburg in the early 1960s.

David Leveaux’s tight, dark and attractively bleak production is derived from Iain Softley’s 1994 movie, in which Ian Hart gave an outstanding performance as John Lennon.

Here, in Softley’s own adaptation with Stephen Jeffreys, Andrew Knott’s jeering, sneering Lennon yields centre stage to the tragic, tortured figure of Nick Blood’s terrific Stuart Sutcliffe.

The two met at Liverpool Art College, and painting always comes first for Stu, especially after he starts a Hamburg romance with Astrid Kirchherr (a lovely performance from lissom Ruta Gedmintas), the blonde photographer who was the group’s first groupie.

The narrative weaves artfully through the hardest, meanest rock ‘n’ roll I’ve ever heard on a West End stage, from Chuck Berry’s “Johnny B Goode,” Little Richard’s “Good Golly, Miss Molly” (with its extraordinary mid-way rhythmic switch) and the Isley Brothers’ “Twist and Shout” all the way to the Beatles’ characteristic first hit, “Love Me Do,” the only song of theirs that is played.

The show’s like a painting itself, conjuring not only Stu’s manic splurges in the style of Jackson Pollock, but the grimy underworld of Hamburg on the Reeperbahn, where the boys played six hours a night for an audience of pimps, rockers and prostitutes, and slept behind a flickering cinema screen.

This use of projections is the weak spot in an otherwise brilliant design by Christopher Oram and Andrew D Edwards, with doubled-up lighting and sound credits, too, for Howard Harrison and David Holmes, and Ed Clarke and Paul Groothuis.

Stu’s tragedy involves escaping John’s clutches and dying too early. The other personnel jolt when the group returns to London comes when record producer George Martin insists that Pete Best is replaced as drummer by Ringo Starr; the show offers no evidence to prove this was a necessary move, and Oliver Bennett’s incensed and deeply hurt Pete is etched with reasonable indignation.

Brian Epstein hovers on the fringes, too, while the fringes themselves complete the definitive post-Hamburg look of the Fab Four kitted out in Astrid’s grey jackets. Daniel Healey sketches in Paul McCartney’s flip intelligence very nicely, and Will Payne is suitably blank, onstage and off, as George Harrison.

This is isn’t just another jukebox musical, nor is it another brain-dead tribute show. It’s a beautifully wrought and darkly cynical evocation of an era, and a particular place, as the Beatles found their inimitable voice through the grit and virility of the pounding music they loved still to play even as their own more lyrical, musically complex compositions poured forth over the next decade. For once, you really do feel like dancing in the aisles at the end.