Writing anything based on another author's characters which is not a straight adaptation always has the dangerous tang of fan-fiction about it, and many a pastiche has fallen by the wayside due to an insufficient knowledge or love of the original. The usual rule, as any Hollywood film-maker knows, is that you must make a damn good job of such things or prepare to be torn limb from limb by rabid fans.

Yet Sir Arthur Conan Doyle's detective has defied time, space, logic, fashion and literary criticism to become one of the most recognisable and beloved characters in fiction: Sherlock Holmes belongs to everyone. He is constantly updated, rebooted and rerouted – and the joy of this show is that it's done with exactly the right mixture of affection and irreverence to please hardcore Holmesians and ordinary punters alike.

It's 1898, and Holmes (Tim Walton) is back from the dead, having survived his dramatic clifftop struggle with arch-enemy Professor Moriarty at the Reichenbach Falls. However, bizarre clues and a spate of dognappings indicate that the Great Detective may not be the only one who has lived to fight another day. Holmes, convinced that Moriarty has returned, prepares to confront his nemesis before winsome artist Bella Spellgrove (Leonie Heath) can get caught in the crossfire.

Too often in a triple-threat musical, where composer, lyricist and bookwriter are the same person, one of those aspects of the show suffers (and usually sucks); but The Revenge of Sherlock Holmes is probably the best-balanced example of the type I've seen. Bricusse's lyrics are witty, complex and sharp where they need to be, sweet when the song demands; his melodies are catchy, hummable and varied enough to retain musical interest, and his book boasts some great gags, characterful, credible dialogue and a cracker of a plot.

Luke Fredericks's peppy, beguiling production pays homage to its venue's history by incorporating elements of music-hall into the show, and this stylistic choice works brilliantly... most of the time. Watson's pre-show warm-up banter segues nicely into the brash, infectious opening number "Sherlock Holmes"; and telling the Reichenbach Falls episode through puppetry, as well as using conjuring in Holmes's song "Look Around You" adds genuine interest, humour and sparkle to these set-pieces.

Dr. Watson (John Cusworth) and Mrs. Hudson (Andrea Miller) as rival divas competing for the limelight is a less successful idea, which eventually descends into shameless mugging by Miller throughout. However, Miller's "randy granny" take on the landlady is undeniably a crowd-pleaser; she has the comic timing and the belt to bring the house down with charm songs like "A Lousy Life" – at the climax of which she's sawn in half. Cusworth also has bags of charm and presence, yet despite looking like John Barrowman's sexier older brother, he's not just a pretty face: his cheerful, gung-ho Watson lights up the stage and garners some of the biggest laughs in songs like "Halcyon Days", a morgue-set duet which recalls the farcical absurdism of a Mel Brooks movie. Besides, any man who can carry off a yellow checked suit and a bowler hat with such panache is one to watch.

It seems rather unfair not to namecheck the whole cast, as they were uniformly excellent, but standouts were Leonie Heath as Bella, whose innocent looks and pure, lyrical soprano belie her character’s complexity; Stephen Leask doubling as Lestrade and Watson’s medic pal Boffy, and Ryan Pidgen as Baker Street Irregular Wiggins.

I was initially doubtful about the casting of a hulking thirty-something as an adolescent urchin, but Wiggins leads a lot of chorus numbers, and the wisdom of this choice soon becomes clear. When the Irregulars (Pidgen, Adam Pendrich and Benjamin Bond) show off their fancy footwork in Lee Proud's precise, vivacious choreography, and Pidgen lets his tiger of a bass-baritone off the leash, the rafters rattle and the floorboards shake – in the best possible way. The three-strong female chorus is also awash with talent and versatility, equally at home going en pointe in a romantic ballet sequence and whooping it up, Lambeth Walk style, in the Oliver!-esque Cockney rhyming song "Apples and Pears".

In fact, I'm willing to bet that if you love My Fair Lady and/or Oliver!, you'll find plenty to like in this show; not least Tim Walton's Rex Harrison-like interpretation of Holmes as a misogynist curmudgeon forced, for once, to let heart rule head as he searches for the missing Bella. His and Cusworth's sprechgesang approach to the songs mostly works, too, but I found myself wishing that the four leads were miked, as anything sung behind the proscenium arch was lost to the blast of the stage-right band (tip: sit on audience right or in the gallery).

But these acoustic issues – plus the fact that, though the show doesn't feel long, at three hours all in, it could stand to lose a few minutes – are minor niggles in a great evening. And when you balance them with Stewart Charlesworth's kaleidoscopic period costumes and ingenious set, and add the contagious air of loving every damn second exuded by the cast, it would be churlish to give this show less than five stars.

It's rare to find a musical even non-musical-fans can love, but with its panto panache, boundless energy, toe-tapping tunes and mischievous sense of fun, The Revenge of Sherlock Holmes is it.

The Revenge of Sherlock Holmes, at Hoxton HallKaty Darby reviews The Revenge of Sherlock Holmes at Hoxton Hall.5