’As we are all solipsists, and all die, the world dies with us,' wrote Anthony Burgess. It is with something like this in mind that Claudia Hampton announces her intention to write A History of the World, a text which quickly digresses into vignettes from her past. She has terminal cancer: Moon Tiger opens with her lying in a hospital bed, IV fluids and her daughter by her side. Only in the disordered flashbacks that accompany her re-appraised memories will she spring out of it.

Slowly, piecemeal, we reconstruct the story of her life. Above all it is a story of relationships. The six-person cast faces two key challenges as a consequence: most of them must play several characters, and all play the same characters at different points in time. They adjust admirably, and much of the play's humour derives from this fact. Jane’s brother Gordon – played by an early-thirties Christopher Brandon – makes apeish faces and scuttles four-legged over the stage; Jade Williams as Lisa flaps her hands breathlessly and begs her mother for a pet baby monkey. Old age is less convincingly suggested by bent-over, stiff-legged poses, though Phil Cumbus playing Jasper is particularly good in this regard. And the multiple-character structure is effectively exploited in the person of Tim Delap, playing only Tom, perhaps the sole true lover in Claudia’s life. Jane Asher herself, also playing only one character (Claudia), is excellent as a forthright, purposeful journalist and popular historian. If at first she strikes us as unsympathetically controlling, it is part of Moon Tiger’s achievement to lend her a likeability and poignancy in the accumulation of her past.

The set, which must represent an array of unusual locations, is salutarily straightforward: a bed, some chairs, and the highlight, a tall screen composed of eight, patterned, semi-opaque panels. Projections on this screen, from the Egyptian desert to scenes (putatively) from Hungary's 1956 revolt, work wonders at suggesting place. Together with varied lighting and some subtle background sounds – bird calls or the chirrup of insects – they create an almost filmic effect. Regretfully a few technical faults, including an unaccountably shaded panel, mar this otherwise inspired mise-en-scène.

Moon Tiger was adapted from Penelope Lively's 1987 Booker Prize-winning novel by Simon Reade, and some its weaknesses can be traced back to that text. Characters like Lazlo, the Hungarian emigrant, are afforded little space for development in the strictures of dramatic form: they might have been cut or combined with others. Hints of an incestuous relationship between Claudia and her brother Gordon are striking but also baffling, and might’ve been expanded upon. And some of Claudia’s pontifications on language – "language is what tethers us to the world"; "we open our mouths and out flow words whose ancestries we do not even know" – are a little tired, better-suited perhaps to novel than play. The real potential of this form lies in the contrasts and parallels it can draw across time and space, in its impressionistic transitions and the gradual emergence of meaning out of fragmentariness. It is its desert love-war subplot, surely an inspiration for Ondaatje’s English Patient, which produces its most powerful scenes. And there is something magnificently nostalgic about its ending – it feels as if we have understood with unusual acuity what it means to have lived a life.