The Cordelia Dream, Wilton's Music Hall, London

The Cordelia dream in the title of Irish playwright Marina Carr's new play for the RSC is that of a Woman who hears the four howls (as opposed to five nevers) in King Lear. Is this Woman, played incisively by Michelle Gomez, Cordelia herself? Is the Man she is visiting, played crazily by David Hargreaves, supposed to be Lear?

Is she dead? Is she a nurse? How long have you got? The two characters remain Man and Woman only. Carr wants the weight of her general thoughts to eclipse the identity of the messengers. They are both musicians. We hear Man's work, a sort of plangent, hysterical modernist mish-mash composed by Conor Linehan, played spiritedly at the side of Wilton's on a string trio against a piano recording.

Man says he is a genius and accuses Woman of being a charlatan. After a fairly compelling first hour, Selina Cartwell's production then deteriorates into a re-run of stale arguments between father and daughter as they exchange clothes and insults and then toast his virility and her silence. They uncork the champagne with a feeble phut, which just about sums it all up. Gomez's face is daubed in blue, to signify death, and the couple dance a dismal waltz to the unlikely seasonal accompaniment of "Silent Night".

In its defence, I'd say the writer is saying something quite interesting, and Celtic, about the need for children to abandon their parents, and the difficulties that arise when an artist feels threatened by his own children. And I like the sound if not substance of Woman's idea that an artist transforms the process of disguise and plagiarism in the necessity of writing something down by an act of faith. But Carr never allows this theme any room to breathe or prosper as Woman is also confined – and defined – by such curious assertions that there's not been a good time to be a woman since the Brontës, and Man hasn't finished a work of any note – or indeed, stave -- for years.

You could imagine a wonderful dramatised bust-up between Kingsley and Martin Amis, say, or Lennox and Michael Berkeley. By the end of Carr's play, which is neither as bad as it sounds nor as good as it should have been, I would have settled for a ding dong between Judy Garland and Liza Minelli, or perhaps even John and Julian Lennon; instead of dealing with the death sentence of working in a great parent's shadow, Carr suggests merely that the parent works towards some kind of salvation in the protracted demise of the offspring. This is a tragic conclusion that the piece, as theatre, simply doesn't earn.

Commissioned to write a response to King Lear as part of last year's Complete Works festival, Carr is left high and dry with a play that only exposes the desperation of the RSC new writing policy and looks ridiculous on the high scaffolded platform in Wilton's, but not as ridiculous as the first play in this season, Adriano Shaplin's The Tragedy of Thomas Hobbes.

Cartwell's production is another dog's dinner, despite the dedicated performances of Gomez and Hargreaves, the latter even bearing the indignity of lying on top of the piano in his underpants – not one of the year's erotic highlights – with a patient shrug. The musicians aren't sufficiently integrated. In fact, I didn't even know they were there until they came on for a bow with their fiddles.

The use of video screens is perfunctory and soon dropped. The perfect acoustic is betrayed in the inside-out standing flats of Giles Cadle's design, which send voices shooting off in all directions. You see how the RSC spends money, but you don't see what's driving the creative engine; it's running on empty.

The second act takes place five years after the first, and the Man has at last completed a concerto for piano and strings called "The Cordelia Dream." But Woman says it sounds like a first draft only, and they're off again, opening old sores and piling up Man's problems with the child he says was goat-faced and dog-hearted with the soul of a snake.

Woman bides her time, but there's no way back from that terrible condemnation; only an exit.

To 10 January (0844 800 1118)