Human Rites, Southwark Playhouse, London <br></br> The Mikado, Orange Tree, Richmond <br></br> Jerome Kern Goes to Hollywood, King's Head, London

Who said that book burning was wrong?
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'Hell is cold. I am in hell! And there's nothing more to say," cries the shivering literature student, Marina, in Human Rites (Les Combustibles) by Amélie Nothomb. Marina is under siege in some freezing city where, we gather, "the Barbarians" are bombing the campus and the only things left to burn are her professor's library and her sexual mores. Both go to blazes as Miriam Hughes's angelic-looking Marina and her ragged post-grad boyfriend (Edmund Kingsley) are embroiled in a destructive ménage à trois with the cynical old prof (Edmund Dehn).

As well as being a première for the Belgian Nothomb, this is the professional debut of Natalie Abrahami - previously assistant director at the Royal Court and Almeida. Her traverse staging, with the audience tightly hemming in the actors, has some notable strengths, including a hint of gladiatorial combat and a spartan beauty. The prof's books hang on delicate wires at one end of the room while a grim industrial bin, serving as a stove, dominates the other. This set is designed by up-and coming Colin Richmond (also responsible for Northampton's excellent Hansel and Gretel, reviewed last week), and Abrahami experiments with choreographic interludes too. The incineration of the tomes turns into a sardonic, clown-like ballet with Marina slowly spinning back and forth on the library stepladder accompanied by the ditty, "If that's all there is,/ Let's keep on dancing". Unfortunately, the cast have not (at this early stage in the run) brought their characters' oscillations, between affection and callousness, into sharp focus. Beyond that, it is hard to see why Abrahami has favoured this script in the first place. Nothomb may be a prolific novelist, honoured with a grand prix by the Académie Française, and her big themes - war and suffering, deprivation and depravation - are ever-pertinent. However, that doesn't make her a decent playwright.

Her nameless war zone feels abstract and unconvincing, and no one is at all likeable. It's hard to care about the incineration of endless authors and titles you've never heard of, and the dialogue (translated by Abrahami) is tiresomely unnatural, veering between the aridly academic and C-rate sexual melodrama. Les Combustibles just left me cold.

Gilbert and Sullivan's The Mikado comes as welcome light relief in a jovially homespun production that ditches the Japanese regalia and sets the action on a modern-day English cricket pitch. The rugby fans of Twickenham feature on the Lord High Executioner's little list and Nanki-Poo, the heir-apparent disguised as a wandering minstrel, is described as a lousy but gorgeous rhythm guitarist.

Dazzling singing isn't the order of the day and director Chris Monks is, of course, not the first to notice the score is scarcely Oriental at all. Yet the loveliness of Sullivan's old English airs comes to the fore in this intimate in-the-round setting. The improvised rigmarole with sporting props can also be charmingly silly, not least Kieran Buckeridge's Pish-Tush presenting a letter on his still-warm box as if it were a silver tray, and Julian Forsyth's droll Mikado pretending to surf on his cricket bat.

Carol Noakes is miscast as the amorous crone, Katisha, being way too elegant and not nearly comical enough, but Sophia Ragavelas' Yum Yum is a teasing schoolgirl with terrific sparkle, waving her come-hither hockey stick. Her duet with James Millard's Nanki-Poo ("This is what I'll never do"), where they aren't allowed to kiss but practice by snogging their deckchairs, is delightfully absurd.

New productions are always thin on the ground in early January, so I'm sorry to report that Jerome Kern Goes to Hollywood really was scraping the barrel and chewing the splinters. This cabaret-style entertainment, accompanied by one piano and double bass, is a celebration of the Broadway composer who collaborated with Oscar Hammerstein on Show Boat. A few scrappy anecdotes are slung in between the songs, the best one relating how Kern once arrived at a Broadway rehearsal and yelled from the stalls that he couldn't recognise his own music, only to be informed he was in the wrong theatre. However, David Kernan's substandard production is cringe-inducing. My eyes were swivelling in their sockets in a desperate attempt to alight on anything other than his appallingly cheesy singers, Sheri Copeland, Jamie Golding and Glyn Kerslake.

Though elegantly dressed and vocally assured, Copeland snaps her meaningless grin on and off like a psychotic robot. Meanwhile, Golding and Kerslake struggle vainly to look suave in their blazers and cravats, like Tweedledee and the Tin Man posing as Gene Kelly and Frank Sinatra. Sickbags ought to be supplied for Kerslake's horrendously self-indulgent, warbling rendition of "The Folks who Live on the Hill".

If you squeeze your eyes shut and listen, most of the evening is tolerable. To Kern's credit, there are many irreducibly great songs in the line-up, ranging from "A Fine Romance" to "Ol' Man River". Thank heavens for the husky veteran Angela Richards who sings "Smoke Gets in Your Eyes" and "All the Things You Are" as if she really feels the yearning behind the lyrics. I hope that's a sufficient response to the final chorus of "Look For the Silver Lining".

'Human Rites': Southwark Playhouse, London SE1 (020 7620 3494), to 22 Jan; 'The Mikado': Orange Tree, Richmond (020 8940 3633), to 12 Feb; 'Jerome Kern Goes to Hollywood': King's Head, London N1 (020 7226 1916), to 20 Feb