Jack Cardiff was a great British cinematographer, the man who shot the first Technicolour film in Europe and filled The Red Shoes and Black Narcissus with saturated, glowing hues. Unless you are over 60 and a movie buff, or both, you may not have heard of him. Even if you have, it's unlikely you would have thought his life story was a suitable subject for a play.

But Terry Johnson did and Prism is a biographical study of the great man, told from the point of view of his declining years when dementia is taking hold and he is slipping back into a past that is colourful in many ways. For Cardiff was not only a master of his art, changing cinema forever, but also an expert seducer of women. His lighting made them beautiful and many of the stars of the day fell happily into his arms in gratitude. "My job is to flatter women," Robert Lindsay as Cardiff explains.

The problem with the play as a drama is that it takes an awful lot of knowledge for granted. It opens with great brio, with voices behind a garage door, discussing the different screen sizes – from Cinemascope to TV - left by its slow rising. Cardiff appears with his son, Mason and Lucy, a newly appointed carer, walking into a room that is hung with images of his own life, which Mason wants him to record in a book.

Johnson, who also directs, wrings comedy as well as pathos out of what Cardiff can and cannot remember. He loses words and has to describe them; he's terrified of losing his sight. The past is more real than his family, particularly his wife Nicola (Claire Skinner), who is desperate because her husband no longer recognises her. His son, Mason (Barnaby Kay) is lost in his father's shadow. Even Lucy the carer is burdened with a tragic home life.

Yet Cardiff's memories of his famous subjects – Katharine Hepburn and Humphrey Bogart on The African Queen, Marilyn Monroe accompanied by her husband Arthur Miller on The Prince and the Showgirl – glimmer in the air. In one wonderful scene the walls of the garage room dissolve and we are plunged on Tim Shortall's set into the jungle, during the filming of The African Queen. That moment of unexpected transformation encapsulates the magic of light and imagination that Cardiff is always describing.

But all too often, Prism feels like a series of anecdotes strung together. They go down beautifully with the Hampstead audience, who are arty enough to get a joke about Robert Bolt that involves knowing (without being told) both the name of his wife and what she did with her urine. Yet I found myself increasingly worried by the fact that so little was explained. The dialogue, for example, talks of Katharine, Audrey and Sophia, but never bothers to add the surnames Hepburn and Loren. It's range of reference is very narrow, even indulgent.

The saving grace of Prism is Lindsay's performance as Cardiff. The play was partly his idea and the role is a gift, giving full rein to his charm, effortless dramatic timing and remarkable ability to convey fleeting and complicated emotion. There's strong support too from Skinner who gets to impersonate Katharine Hepburn, and from Rebecca Night who is transformed from carer into Monroe and Lauren Bacall. But it's Lindsay's night.

Prism runs at Hampstead Theatre until 14 October.