Comedian/presenter Graham Norton once filmed a sequence in the flagship Tokyo store of the Hello Kitty merchandise empire. Taking an imaginary call on a Hello Kitty phone, he intoned gravely, “I’m afraid Kitty can’t speak to you... Well, she has no mouth.” Kitty in this play has no mouth either, and never appears onstage, yet the piece is all about her: about the overwrought nervous distress which keeps this iconic screen actress from completing her movie currently in mid-shoot and about the attempts by those around her to persuade her to make the effort.

Stephen Billington tempers the safari-suited director’s machismo with genuine but not limitless concern. Oliver Le Sueur’s producer, inexperienced in the ways of film, is the nearest we have to a viewpoint character; Jeremy Drakes as the screenwriter and Kitty’s husband cares, too, but can’t express it competently, so no wonder their marriage is foundering.

You may possibly have twigged that this is loosely based on the true story of The Misfits, Marilyn Monroe’s final film made in 1960, directed by John Huston and written by then-husband Arthur Miller. (It’s simpler to use their real names here than the characters’.) This play, too, is by Miller; it is the last one he wrote, premièring in Chicago in 2004 a few months before his death. This attentive production by Phil Willmott is its second ever.

Miller’s penultimate play, Resurrection Blues, seen in London in 2006 in a shambolic production by Robert Altman, was an almighty mess. Finishing The Picture isn’t, by any means, but nor is it the high final note his career deserves. Forty years on from his After The Fall, he returned to trying to explain – not excuse, not quite – the disintegration of his relationship with Monroe, alias Kitty. Here, he reserves his full venom for her Method acting gurus Lee and Paula Strasberg, whom he portrays as self-aggrandising, waffling pests. Yet Miller the playwright’s concern for Monroe seems as effortful as that of Paul, the Miller character. The biggest surprise, puzzle and disappointment is that, for someone so evidently haunted by the memory, Miller can in the end (literally, for him, the end) offer so little unique insight.

Written for the Financial Times.