Ben and Imo are composer Benjamin Britten and his musical assistant, Imogen Holst. But those cosy pet names tell us where we stand – or at least, where we think we do. The illusion of being inside an artistic clique is at the heart of Mark Ravenhill’s new two-hander, which began life as a BBC radio drama and which he has now opened out into a two-act play about the pair. Alan Bennett did a Britten play a few years back but Ravenhill is sharper, and as directed by Erica Whyman, Ben and Imo just about supports its own length.

His Benjamin Britten is bravura – neck stretching forward, then springing back, like a tortoise

Which is more than can be said for its subject, Britten’s 1953 coronation opera Gloriana. Ben (Samuel Barnett) is on deadline, stalling desperately over the big national commission that he’s claimed as of right, but which is turning out to be an albatross. Imo (Victoria Yeates) breezes in with her life packed into three carpet bags; forced upon the reluctant composer by the anxious commissioners and tasked with helping him to get Gloriana done. The heart promptly sinks: free spirit liberates uptight genius? Brilliant woman rescues stale pale male? Been there, done that, usually while listening to a BBC radio play.

But Manic Pixie Dream Girls weren’t really Britten’s thing (even when they were the daughter of Gustav Holst) and Ravenhill has something more interesting in mind. The long debates between the two have a boisterous, bracing intellectual energy, and they’re frequently very funny. A useful side effect of the authentically rendered 1950s setting (designs and costumes are by Soutra Gilmour and they’re very brown) is that expletives are suddenly rude again.

Gloriana was a rare Britten misfire, and it’s to Ravenhill’s credit that he doesn’t endorse the Aldeburgh mythology of a bold masterpiece misunderstood by establishment stiffs, or pursue the notion that Imo was a comparably gifted composer (‘I’m not good enough’, she says, and that’s that). Anyway, no great reversal occurs. Ben knows he’s a nightmare and he doesn’t change. He warns Imo at the outset that he’s selfish, needy and cruel; and in due course she experiences his dark side at storm-force. He won’t grow up while she – crippled by mummy issues and hero-worship of ‘Gussie’, her dead father – simply can’t. But there are limits to her openness: she won’t let Ben visit her bedsit. Meanwhile the North Sea – by turns lulling and violent – plays a passacaglia on the soundtrack.

This Dream is playful, gorgeous to watch, and with Baynton on sublime comic form as Bottom

Yeates is note-perfect as the no-nonsense, jolly-hockey-sticks do-er and organiser: the sort of person whom everyone assumes is unsinkable until an unanticipated barrier shoots up or a tear suddenly appears, and is just as briskly dabbed away. She’s exuberant and expansive, dancing barefoot around Ben’s piano before wheeling offstage altogether. Barnett stands there like he wants to disappear, arms folded tightly against all this unconstrained physicality. His clenched, petulant Ben is a bravura piece of characterisation – neck stretching forward in curiosity, then springing defensively back, like a tortoise. A quizzical, wary expression is his default: a holding position while he decides whether to melt into a shy smile or flash into spiteful rage. He’s compelling; they both are. Still, ‘what is it actually about?’ asked my companion, and that’s not easy to answer. Ideas about duty, about authorship, about Britishness and about Britten-ishness repeatedly break surface to be tossed about like flotsam before sinking again beneath the flood tide of the central relationship. At its core, Ben and Imo feels like a spirited, knowing study of two personalities who together add up to a single functioning artist. It’s engrossing, if a little unanchored. But in Whyman’s production, and with this cast, that might be enough.

Over in the big room, the RSC is staging A Midsummer Night’s Dream – not Britten’s opera; the earlier version, by a local author. Psychedelic is the easiest description of Eleanor Rhodes’s production but in truth it’s a cheerful, multicoloured pop-cultural swap-shop. Oberon (Bally Gill) is a new romantic, Rosie Sheehy is a gutsy, punky Puck with blue hair and a nice line in deadpan eye-rolls, and Matthew Baynton channels Keith Moon as Bottom, willowy and witty in his grooviest Savile Row threads.

Baynton hoovers up the focus in every scene he’s in. This is possibly the only Midsummer Night’s Dream you’ll ever see in which Bottom is the most articulate character on stage (as is often the way at the RSC, the young romantic leads gabble and shout their lines). This Dream is more about humour than enchantment. But it’s playful, it’s gorgeous to watch, and with Baynton on sublime comic form, you could almost wish that Shakespeare had given us more Pyramus and Thisbe, which is saying something.