Theatre review: The Book of Mormon - Lord, they move in hilarious ways

Trey Parker and Matt Stone, the American duo behind the gleefully rude, animated sitcom South Park, have romped into London's West End to cock a snook at religious claptrap. Their satirical musical The Book of Mormon, written in league with Avenue Q's Robert Lopez, wowed Broadway in 2011. All the signs are that it will, surer than Hell, be a long-running hit here too.

Co-directed by choreographer Casey Nicholaw, Parker's production is frequently a blast, with song-and-dance numbers pastiching golden-oldie musicals and its buoyant cast hitting the high notes while keeping tongue in cheek.

At root, this is a 21st-century variation on Candide, a tale of ludicrous optimism following the adventures of Elder Price and Elder Cunningham, a pair of idiotically naïve and blithely neo-imperialist Mormon missionaries sent from squeaky-clean Utah to contemporary Uganda. Here, the locals are shown as less inclined to hymn God's praises than give him the finger for the Third-World troubles heaped upon them.

A living cartoon, Gavin Creel's Price is a tall, handsome zealot with a plastic grin and nerdily quiffed hair. In fact, Creel could be the young Jim Carrey. He's also a fit dancer adding dweeby twists to his moves, tap-dancing and happy-clapping with precision-tooled comic timing.

His sidekick, Jared Gertner's Cunningham, is a tubby, flailing eager beaver. With a none too firm grasp on Mormon theology, he has a scandalous habit of making up wacko stuff – such as that, erm, raping a frog rather than a baby will cure you of Aids.

But as Parker and Stone are at pains to point out, it's hard to take the Mormon founding father's word for gospel truth in the first place. Joseph Smith Jnr was apparently instructed by an angel, in 1820s upstate New York, to nip outside and dig up an ancient sacred text, written on gold plates in "reformed Egyptian" which only he was allowed to see, and which recounted how Christ materialised in America shortly after being crucified.

Obviously not for the pious, the show is splattered with four-letter words and almost begs to be branded offensive. That said, the satire is rarely scorching. Most of the characters are really quite sweet. Jerry Springer the Opera was more outré and the Church of Latter-Day Saints is a pretty soft target. So maybe don't believe all the hype.

In The Winslow Boy (Old Vic, London ****), an Edwardian father is convinced that his adolescent son, Ronnie – a naval cadet – is telling the truth and has been wrongly accused of stealing and forgery. Determined to fight the Admiralty, whatever the cost to himself and his family, Arthur Winslow's battle for justice becomes a cause célèbre (based a on a real case). Confined to the Winslows' drawing room, Terence Rattigan's classic quite brilliantly combines domestic intimacy with moral arguments and ferocious legal interrogations.

Lindsay Posner's revival has one or two mannered moments, and perhaps it would be more intriguing if there were doubt about the innocence of Charlie Rowe's fresh-faced Ronnie. Cavils aside, Henry Goodman is tremendous – dignified and warmly humorous as Arthur, with Deborah Findlay as his long-suffering wife. Furthermore, Peter Sullivan is hilarious and electrifying as the icily swish lawyer who might win the case. Well worth seeing.

In Proof (Menier, London *****), verification should be possible, or so the title implies. Yet can the largely home-taught twenty-something, Catherine, be the author of an ingenious new prime-numbers theorem, as she claims? Or are the inspired equations, stashed in a bottom drawer in her father Robert's study, actually his?

His University of Chicago protégé, Hal, isn't sure what to believe, having come to Robert's house soon after his death to comb through his papers. Though a dazzling mathematician as a young man, Robert latterly suffered debilitating mental breakdowns. We gather that, while delusional and attempting to decode messages from aliens, he was cared for devotedly by Catherine. Hal (Jamie Parker) finds himself drawn to her but she may – besides suffering from depressed exhaustion – have inherited her father's chronic instability. Jetting in from New York, her sister is belatedly determined to mollycoddle her, or perhaps just drive her round the bend.

David Auburn's Pulitzer-winning teaser has not aged badly since its Donmar premiere with Gywneth Paltrow more than a decade ago. In fact, I think I prefer this quietly excellent Menier staging, directed by fast-rising Polly Findlay. It's played out in the scrubby backyard of a clapboard house, the acting exquisitely downplayed, avoiding sinister melodrama or geeky stereotyping.

Matthew Marsh's Robert, seen in flashback, is never obviously raving, but instead is subtly mercurial, concealing a bullying insecurity under paternal fondness. It also seems credible in this production that Mariah Gale's Catherine could be a genuine maths prodigy, played with an air of sphinx-like detachment, masking grief-stricken desperation and a sharp wit.

The script strains slightly to explain why the proof's authorship can't be verified. But the dialogue is surprisingly entertaining and infused with what seems an authentic understanding of how it feels to be passionate about maths. Equally, Parker and Gale's sexual attraction is heartstoppingly tender and true. Highly recommended.

'The Book of Mormon' (0844 482 5110) booking to Jan 2014. 'The Winslow Boy' (0844 871 7628) to 25 May. 'Proof' (020-7378 1713) to 27 Apr

Critic's Choice

Mies Julie is an erotically scorching South African take on Strindberg's Miss Julie, running at London's Riverside Studios (to 19 May). Pam Gems's biomusical Piaf, starring Frances Ruffelle as the fiesty French chanteuse, is enjoying an extended run at Leicester's Curve (now to 6 Apr).