Greenland, NT Lyttelton, LondonLess Than Kind, Jermyn Street, LondonAccolade, Finborough, London

Drama-by-committee is always doomed to inconsistency. But at least the National Theatre isn't afraid to dive into the great issue of the age

Whoops, we forgot to save the Earth. David Cameron declared that he wished to head the greenest government ever.

If he seriously intends to be an eco-hero, he'd better get his skates on – before much more polar ice melts.

British theatre, in the interim, is making dramas out of the climate change crisis which – remember? – Chris Huhne also called "the greatest challenge facing mankind" when he took office and talked of speedy remediations, last May.

Three cheers for the NT's spirit of political engagement, at least. After its 2010 hit, Earthquakes in London, comes another premiere, Greenland. This one follows a postgraduate called Lisa who ditches her course to become an environmental protester; an Arctic wildlife observer; and a climatologist, Ray, (Peter McDonald) who shows a newly adjusted forecast of devastating global warming to Lyndsey Marshal's Phoebe. She is, we gather, an aide to Ed Miliband.

Alas, though, this production is only a curate's egg. The commissioning of four co-writers – Moira Buffini, Matt Charman, Penelope Skinner and Jack Thorne – probably doomed Greenland's script to patchiness. Lisa's tiffs with her parents are particularly hackneyed, and another storyline, about a lad winning a quiz, seems an unclear metaphor.

Moreover, though inspired by months of interviews with scientists, politicians and campaigners, Greenland problematically yokes facts and fictional (or fictionalised) characters. Some bits sound like verbatim docudrama, accompanied by potent statistics and diagrams. Notably spotlit is the Great Pacific Garbage Patch: the floating cluster of foodchain-polluting plastic litter, now estimated to be the size of France. A mini-lecture by Ray also reasserts the validity of the disputed "hockey-stick graph" of the past 1,000 years, showing soaring industrial-era temperatures.

However, I came away unsure how realistic Ray's extreme predictions for the 21st century were (with the dialogue stressing they weren't ready for peer review). Ethically, it's disappointing too when, falling for Phoebe, he drops out of climate research in favour of fatherhood – heedless of overpopulation fears.

That said, the acting is admirable. Director Bijan Sheibani and his design team also do their best to conceal the script's flaws with imaginative visuals: hatches of golden light opening in a wall of darkness; Copenhagen climate conference delegates dancing under a snowstorm of swirling procedural papers; a polar bear prowling across the stage.

Thought-provoking debates will surely arise in the accompanying series of NT platform talks, by the climate-change sceptics Bjorn Lomborg and Nigel Lawson, among others.

In Less Than Kind, a "lost" 1940s play by Terence Rattigan, Sir John Fletcher is a right-wing industrialist promoted to the wartime cabinet, procuring tanks. Michael Simkins's pinstriped Sir John is happily keeping his mistress, Sara Crowe's Olivia, in style in Westminster, but then her evacuee son (David Osmond), moves in. Sir John, finding himself reviled by this bolshy teenage "pinko", sneakily discovers Michael's own weak spot for women and wads of cash.

An intriguing kick-off for Rattigan's centenary year, Less Than Kind has, as such, never been staged before because he rewrote and renamed it Love in Idleness, reducing the political aggro and making Sir John nicer. Now its belated premiere, directed by Adrian Brown, might surely play Rattigan's "happy" ending with a more satirical, dark edge. Crowe could give the mistress more edge, torn between her guilty conscience and new life. Her son's earlier antics, aping Hamlet, seem merely silly.

Cavils aside, Less Than Kind is sharp on left-wingers selling out and on deals struck to attain domestic bliss. Caroline Head glitters as Sir John's ritzy and canny wife, seeking a lucrative divorce settlement, and Simkins is superbly comical and complicated as he kicks off his shoes on Olivia's settee. Knackered by his workload, he's patient then explosively bigoted, genuinely loving and very nearly heartbroken.

Accolade is an even better play: a forgotten gem written by Emlyn Williams in 1950. Will Trenting (Aden Gillett) is an esteemed novelist with an upper-class wife and a book-lined house near Regent's Park. Yet just as he's awarded a knighthood, he's threatened with an exposé of his other life – slumming it at drunken, "dirty parties" in Rotherhithe.

Williams's play is quietly radical in its presentation of the Trentings' open marriage which, in Blanche McIntyre's strongly cast and understated production, appears to be happy and loving. That's until Graham Seed's greasy, blackmailing Daker arrives. Saskia Wickham is splendid as the plummy liberal pragmatist, Rona. Gillett is also challengingly free of shame, rejecting his publisher's outrage with the argument that he's never concealed his rovings from his wife and they've fed directly into his books.

Barring a modicum of moralising, Accolade is humorous, humane and subtle in its suspenseful twists, and McIntyre's up-close staging enthralls. A talented young director and an exceptional fringe revival.

'Greenland' (020-7452 3000) to 2 Apr; 'Less Than Kind' (020-7287 2875) to 12 Feb; 'Accolade' (0844 847 1652) to 26 Feb

Next Week:

Kate Bassett comes face to face with a climate-change sceptic, in The Heretic

Theatre Choice

At London's Almeida, Becky Shaw is an entertaining, sardonic US sitcom, slick with an element of menace (to 5 Mar). Meanwhile, Daniel Kitson's tour of The Interminable Suicide of Gregory Church, an intriguing tragi-comic yarn, tours to The Junction in Cambridge (Wed), Warwick Arts Centre (Thurs) and Reading's South Street Arts Centre (Fri).