AND lo, the gods of Broadway did find a work of box-office gold and send it forth to London. Yet there was trepidation amongst them, for the dustbin of history is littered with stateside hits that got lost in translation. What reception would the British public give Trey Parker and Matt Stone’s “The Book of Mormon”? Would they get the joke?

Last week these fears were laid to rest. Producers announced that the musical satire from the creators of “South Park” had broken West End records, taking more than £2m ($3m) in sales in a single day after the release of more tickets. Following its official opening on March 21st, it is no longer a question of whether it will work in Britain, but why it is working so well.

One can understand the initial concerns. The show, about a pair of hapless missionaries spreading the word of God in Uganda, is a skewering of the Mormon faith, a Christian denomination founded in 19th-century America which has relatively little exposure on these shores. British critics have pointed out that the show is consistently crude, with racial stereotypes that might be politely described as “broad”. And, bearing in mind that many Brits are schmaltz-intolerant, it is saccharine in the extreme.

Despite these objections (or, perhaps, because of them) “The Book of Mormon” is succeeding. Primarily, the production has enough wit and chutzpah, particularly in Robert Lopez's songs, to pull it off. Who could sit stony-faced through the missionaries’ extravagantly camp rendition of “Turn It Off”, a number about repressing homosexual urges, or “Spooky Mormon Hell Dream”, where a guilty acolyte shares a reluctant dance with Hitler and some familiar green-and-white coffee cups?

The cast’s handling of this material, performed against Scott Pask’s set of shanty homes and torn-cloth sky, does not falter. Even if the gleefully shallow characterisation eventually stymies the show, preventing an entirely satisfactory conclusion, there is no denying the approach pays great dividends in the first half as Elder Price and Elder Cunningham set out on their naive quest.

Although the idea of a satirical musical about uneducated Africans and the Church of Jesus Christ of Latter-day Saints might sound like a disaster waiting to happen, it is, in fact, a reasonably safe bet in the hands of Mr Parker and Mr Stone. The pair spent the last 16 years disguising sharp social commentary as slack-jawed idiocy in their animated television series “South Park”, so audiences know what they are letting themselves in for.

Above all, the show works in London because it plays perfectly to a British sense of cultural superiority. West End audiences delight in frequent references to “the ancient America of biblical times”. They relish—with the doomed acuity that a lifetime of rained-off summer parties brings—the prospect of these cheery, idealistic missionaries discovering that Uganda is not, as they imagine, like “The Lion King”. They scoff at the missionaries’ egocentric worldview as the chorus sings “I Am Africa”, and laugh at the dubious proofs on which their beliefs are founded. For the duration, unfair as it is, these Mormons represent all Americans everywhere.

So yes, “The Book of Mormon” translates just fine. Its producers have nothing to fear. But they are not the only ones hoping to win British hearts and minds through the show. Three full-page adverts taken out by the church appear in the theatrical programme; each one shows a smiling, regular person with a certain religious text in the foreground. “You’ve seen the show,” reads the slogan, “now read the book.”

“The Book of Mormon” is at the Prince of Wales Theatre in London. Now booking until January 2014