As the debate about educational standards and Free Schools rumbles on, the Bush Theatre in west London has had the good idea (gold star guys) of beginning the year with a mini-season of two plays on the subject of education. The first play, by John Donnelly, opened tonight and looks at what happens when a young teacher, Zoe, bites off more than she can chew. It's a thrilling start to the playwriting new year.

Joseph Mallord William Turner - Billy to his intimates, such as he had - is the notional centre of The Painter, a snapshot of the great British landscape artist as a young iceberg. Toby Jones is the main draw in this world premiere of Rebecca Lenkiewicz's new play, and he emanates quiet charisma and sardonic wit. But it's the women in his life who get the better scenes and who steal the show.

Success came early to Turner. In 1799, when the play begins, he was still in his mid-twenties but had been exhibiting watercolours at the Royal Academy for nearly a decade – possibly buying his paints from the Colourworks Reeves factory in Dalston, north-east London, a building which, in a very neat marketing manoeuvre, is also the Arcola Theatre's brand-new premises; a high-ceilinged, unfinished but striking bare-brick space.

There was more going on that year. Turner had just moved into a new studio with his devoted father whom the play and performances induce you to take for a kindly, devoted manservant until late in the game. His mother, Mary, meanwhile, was drifting into madness. In 1799 she entered Saint Luke's Hospital, but would die in Bedlam.

This was also the probable year of Turner's best-known self-portrait (pictured above), deliberately channelled in the publicity shot (pictured left) of Jones for the Arcola's production. But painted Turner is handsome, romantic - intense, to be sure, but also a little suave and patrician. Jones's Turner is unshaven, rumpled, scowling, a bit of rough. When he opens his gob, he's pure East End barrow boy. "I thought Turner was posh!" sighed a woman behind me.

Turner's father, we learn, was from the lower orders: a wig-maker who lost his trade when wigs fell from fashion, one reason no doubt for his devoted support of his son as a new meal ticket. There are also references to a world in turmoil ("Town was mad again") from the Napoleonic Wars, and Turner is cramming Dutch, perhaps on account of his lifelong passion for Holland's art. Rebecca Lenkiewicz's play is full of such elliptical detail. But - with only seven characters - it's very much a chamber piece.

As a rule, Turner didn't do portraits. In the play, he calls it "face painting". He didn't do people much, come to that. "Your heart's a hole, Billy," his mother says. The short, fragmented scenes make it hard to engage with the character, particularly in the first half (under the aegis of the Arcola Theatre's artistic director Mehmet Ergen, the scene changes in this almost-in-the-round production aren't always as swiftly and smoothly managed as they could be).

From time to time Turner holds forth to the members of the Royal Academy on his theories of art, full of contempt for the no-talent nobs, his mind never quite on the task in hand. Then, at the end, he turns to address the audience on his breathtakingly ahead-of-its-time Hannibal Crossing the Alps (1810-1812, now in the Tate Britain and pictured right): "The sun is God and it's a battle. Or dark against light... And... the light has to win."

This should be Turner's big, redeeming, barnstorming speech: a transcendent vision of sublimity, the victory of hope over despair. But at first you assume it's just another of his boring lectures. And far from being the intended coup de théâtre, you can barely make out the slide projection of the painting on the back wall.

So look to the women to pick up the slack. The play has three of them. Turner's mother, Mary (Amanda Boxer) lost her wits when she lost her adored daughter; her son treats her ambivalently and she returns the favour. Jenny Cole, an Irish prostitute (Denise Gough), poses for him and they form an intimate, curiously Platonic relationship which he ultimately betrays.

Sarah Danby (Niamh Cusack), a widowed actress clinging onto respectability, tries to domesticate Turner and unsurprisingly finds him a lost cause. They are all - especially the first two - given stonking, emotional scenes. In a production bursting overall with talent and ideas, all that's needed is for Turner's elusive being, as mazey as his explosions of painterly light, to be brought more clearly into focus.

We remember JM Barrie as the creator of Peter Pan, that quintessentially English fairy story which features Neverland, the Boy Who Wouldn’t Grow Up, and where “to die would be an awfully big adventure”. Generations have embraced this mythical tale as an expression of the spirit of upper-class Deep England. Here the Victorians are us. But James Matthew Barrie himself was the child of a Scottish Calvinist working-class family, and is the subject of Alexander Wright’s play — a hit in Edinburgh last year — which aspires to be a kind of anti-myth.

Problematic in performance in a way that the “problem plays” simply aren’t, Shakespeare’s Roman plays remain some of his hardest to stage satisfactorily. Updated versions too often turn into Magritte-esque fantasies of identikit, suited politicos, while the togas of more traditional approaches can feel absurd, unavoidably laden with satiric or Hollywood associations.

I suspect there is a different production waiting to be unveiled for Witold Gombrowicz’s 1938 black comedy Ivona, Princess of Burgundia. Under the arches at Waterloo, tucked beside the station down a dark and dank service road is the Network Theatre. Home for half the year to amateur theatre, it also now hosts professionals such as Sturdy Beggars, a fledgling group set up by post-grads from The Poor School drama training space at King’s Cross. A complete surprise to me, the Network Theatre boasts one of the finest pair of red velvet stage curtains you’re likely to see in London, suggesting a rich theatricality to come. And so in Ivona it proves in some aspects, if not in others.

The world of the media offers plenty of opportunities for satire, but the idea of a comedy about sub-editors at first glance seems odd. After all, the sub-editors, or subs, are hardly journalism’s most glamorous beings: these office-bound nerds spend their working days correcting the spellings of journalists and cutting their copy, while penning pun-heavy headlines and writing captions to pictures. Yet, as R J Purdey’s play - which was a sellout hit at this venue last year and now returns for another run - makes clear, there is some comic juice to be squeezed out of the dreams and tribulations of these worker ants.

Vienna has its New Year's Day concert, conducted this year with some style but not quite enough sensuousness by Franz Welser-Möst. London could do worse for a more modest equivalent than let the Wooden O play host to a well-spiced small package of carols, seasonal songs and readings from Chaucer's times to Thomas Hardy's. But sing and play it lustily, ye Gabrieli ladies and gentlemen, or not at all. And it's sad to report that the proceedings got off to a start as soggy as the winter's afternoon they were supposed to keep at bay.

"Bliss was it in that dawn to be alive," trilled critic Harold Hobson in Wordsworthian mood about a musical which even in 1954 must have made Gilbert and Sullivan look like Ingmar Bergman. Over half a century on, can Salad Days's sweetly silly paradise be regained? The fact that my eyes pricked as the two lovers launched into the dance-song celebrating their magic piano may partly be ascribed to nostalgia for teenage am-dram - late Seventies, not early Fifties - but much more to the airy lack of irony in Tête à Tête's deliciously classical production.

A night when a fresh fall of snow was fluttering from the heavens could hardly have felt more fitting for the opening of this Shakespearean romance – particularly since David Farr’s production for the RSC, first seen in Stratford in 2009, so felicitously counters fire with ice. Cruelty and rage, the willful closing off of the heart, the reawakening of hope and the resurrection of enduring love: passion both kills and sustains in the worlds of Sicilia and Bohemia; and if the staging sometimes seems slightly ponderous, it delivers moments of arresting intensity.

London is a magical place at this time of year - so many streets with their individual lighting schemes and colours, and nowhere I think is lovelier than the new-look Southbank Centre, where from the side of the Festival Hall swings a spacious canopy of silver-blue trickles reflected in the glass of the new cafés alongside, a captivating, super-chic Thames-side installation. Into this urban grotto last night Kneehigh Theatre’s bouncy, folksy Hansel and Gretel came as welcome as a homemade mince pie.