The salty strains of Benjamin Britten's opera Peter Grimes open and close Zoe Lewis's new play about the composer's stay in New York at the start of World War II, and that great work will open to great acclaim in 1945, and plays to this day. But it is the 1941 flop Paul Bunyan that preoccupies him and his collaborator, W.H. Auden, in the louche, 24-hour party apartment that they share in Middagh Street.

Britten in Brooklyn takes on big themes: the illicit relationship between Britten and the tenor Peter Pears, pacificism, and the role of the artist at a time of war, against a colourful backdrop of the carefree living at which unlikely flat-sharers work so hard. With Britten the nervy newcomer, Auden runs a chaotic household where the plumbing is so erratic you can boil an egg in the lavatory, and where drink and pills matter more than the dinner at which politics talk is banned.

Crashing through this heady household are the stripper Gypsy Rose Lee and tomboy writer Carson McCullers, in and out of love with each other, but mostly in love with themselves, and in McCullers's case, like Britten, on the verge of an artistic breakthrough. That's four big personalities in one small space, until the arrival of a stony British naval officer.

The Gypsy/Carson tango feels like a sideshow, and it is a little wearing, but without it, Britten in Brooklyn would run dangerously close to being a second bite at the Britten/Auden story that Alan Bennett pretty much buttoned up in The Habit of Art at the National Theatre seven years ago. It is also a vehicle for a somewhat mannered Sadie Frost in a range of cross-cut eveningwear as Gypsy, working again with Zoe Lewis; the pair collaborated in 2012 on the one-woman show Touched… Like a Virgin.

But there are solid performances from Ruby Bentall as Carson and John Hollingsworth as Auden, while Ryan Sampson's Britten, if a little eager, reminds us that national treasures do not emerge fully formed.

The frustration is that in an apartment that is supposed to be a permanent state of whoopie, and with a grand piano brought in specially, according to Auden, there are few glimpses of Britten the composer not only of opera but of the sly Cabaret Songs. Only his Funeral Blues ("Stop all the clocks ...) is briefly reprised.

Cecilia Carey's vibrant design and Oli Rose's brisk direction sustain the spinning alternative world that the artists inhabit while those outside are concerned with the harsh realities of war. The play's great strength is in showing how easily high-minded principles can appear merely self-indulgent and shiftless to the sober onlooker.