There’s been no escaping the mormons, seek at least if you’re anywhere near London, where the arrival of The Book of Mormon from Broadway has been preceded by an massive marketing assault. It has raised consciousness but also expectations to an unprecedented degree — can it be as good as it promises? Or as shocking as some fear (or hope)?

Actually, the most surprising thing about it is how sweet-natured and conventional it is, beneath its hard-edged, sometimes gratuitously potty-mouthed surface. As it follows two eager young missionaries despatched from Salt Lake City to Northern Uganda to convert the variously downtrodden locals — 80% of them have AIDS, and the local warlord is hellbent on enforcing female circumcision — to their religion, they sing, “This book will change your life!”

The show won’t change yours, but it is a lot of fun, and works on a number of knowing levels. On the one hand, of course, there’s the deliberately coarse, outrageous but courageous comic satire of South Park creators Trey Parker and Matt Stone, who have co-written it with Robert Lopez (co-writer of the musical Avenue Q). Nothing is taboo as it launches attacks on religious belief, sexual hypocrisy and the familiar cliches of musical theatre itself.

But though it sometimes tries too strenuously to shock, some songs outstay their welcome and at other times it is played too knowingly, there’s an irresistible fondness, too, that prevents it ever becoming truly dangerous. Instead, it is mostly a blast of goofy, glorious comic delight.

The clean-cut Gavin Creel and the comically nerdy Jared Gertner, both imported from the US, make a blissful study in contrasts as the two new missionaries, and they’re joined by an irrepressible, irresistible local company of mormons and Africans, including particularly terrific contributions from Stephen Ashfield, Alexia Khadime, Chris Jarman and Giles Terera.

They have been drilled to perfection in Trey Parker and Casey Nicholaw’s production that makes it feel like a modern-day Guys and Dolls. Just as that show saw Salvation Army missionaries trying to convert professional gamblers around Times Square to the gospel, these mormons face a seemingly harder task.

But the show achieves another, even more unlikely act of conversion: here’s a musical that puts itself triumphantly in the middle of the cultural conversation. Anything that does is enough to make me a believer.