I do my level best to avoid Mormon missionaries. If I see them coming, I cross the street, and if they try to continue talking to me after the first polite rebuff, I tend to ignore them; to me, there is something quite offensive about the idea of going up to a complete stranger and, essentially, telling them that your belief system is better than theirs – not to mention that if you really want to try to make the world a better place, there are plenty of more constructive ways to do it than hanging around on street corners and at bus stops pestering complete strangers about a myth. The Book of Mormon, a new musical by the co-creators of South Park and one of the writers behind Avenue Q, is thankfully far more entertaining than your average encounter with a pair of Mormon missionaries (not difficult, so are most migraines), and it’s arrived on this side of the Atlantic trailing clouds of hype (and ticket sales) that are hard to dismiss. Everywhere it’s played so far, it’s received ecstatic reviews, and everywhere it’s played so far, it’s been formidably difficult to get a ticket. Ticket sales in London are heading in the same direction – best availability is several months from now, and preview performances were almost sold out within days of going on sale – but does the show itself live up to the publicity?

In a word, yes, which makes a nice change. Unlike the last show that was touted by the Broadway critics as the second coming of musical comedy – The Producers, which was never as successful anywhere else as it was on Broadway, and which suffered in the absence of its two original stars – The Book of Mormon appears to be a durable enough show to succeed without the original Broadway cast. In London we have a pair of leads imported from the States – Gavin Creel and Jared Gertner, neither of whom is the originator of their role – as Elders Price and Cunningham, two Mormon missionaries who are sent to try and convert the people of Uganda, alongside an entirely local ensemble. They’re all great – this cast is giving as smart, sharp, and funny a set of performances as you could ever hope to see – but none of them are stars (although all of them probably should be), and it doesn’t matter in the slightest. When they’re replaced – which they will be, the London production is going to be around for a while – the show will play just as well with whoever is next, provided the resident directors and stage management run a tight ship.

The reason is simple: this show is flat-out funny. It’s also gleefully, lethally rude, taking deadly aim at an extraordinarily broad range of targets from the absurdity of the Book of Mormon itself and religious dogma in general, through Western colonialist attitudes to the developing world (in the second act, Bono gets a well-deserved kicking), to The Lion King, with healthy doses of profanity and gross-out humour along the way (it contains, among other things, a rectal insertion joke that has to be seen to be believed, and which made me laugh so hard that it caused me actual physical discomfort). No stone remains unturned, and no sacred cow goes unmolested – but there’s also a point, and the writers pull off a difficult trick: despite the barrage of satirical/scatological humour, this is at core a surprisingly sweet show that has something quite surprising to say about the power of faith. To say too much more would be to give too much away, and the show is certainly loudly and consistently critical of rigidly dogmatic religious leaders, but it’s a far cleverer piece of writing, in terms of the stance it takes towards its subject-matter, than you might expect. For that matter, it’s also a far cleverer piece of writing than Parker and Stone’s South Park: Bigger, Longer, and Uncut or Team America: World Police, both of which – while undeniably very, very funny – are firmly rooted in the blunt-instrument school of satire. Here, while nobody is above making scrotum jokes, there is something a bit more thoughtful going on, although there is never (thank God) a “but seriously though, folks” moment anywhere in the script, and the payoff at the end of the show is surprisingly touching.

How good is it? Well, I think the last musical that made me laugh as much was City of Angels, coincidentally at the same theatre, and that was twenty years ago (omigod, I’m getting old) – and that show, unlike this one, backs itself into a plot corner in the second act and relies on a not-very-convincing deus-ex-machina to get out of it. The Book of Mormon isn’t a perfect show either – while the direction (by co-writer Trey Parker and Casey Nicolaw) and choreography (by Nicholaw) are both blissfully sharp, the physical production (sets by Scott Pask, costumes by Ann Roth, lighting by Brian McDevitt) tends towards the functional, despite a few very clever visual-comedy flourishes. And the score, while always tuneful and always entertaining, peaks early, in that the opening number (‘Hello’, a piece of extended counterpoint in which the would-be missionaries practice their spiel) is better than almost anything else – this might be one of the all-time funniest musicals, but it’s not one of the all-time great scores, although the cast recording is enormous fun. The pace flags a bit, too, in the first half of the second act, but I saw a preview, and it could very well be that that will change as performances are adjusted in the run up to the press night.

Those are minor quibbles, though, and I’m picky: the biggest thing wrong with The Book of Mormon is simply that top-price tickets are priced north of £60 and it’s sold out for months, which means it’s going to be a while before I get to see it again. The best musical comedies – and they are few and far between – leave you walking out of the theatre feeling as though you’re floating on air. On that count, The Book of Mormon unquestionably delivers.