The disappearing Frummer

David Rodinsky's room, an attic above a synagogue in Spitalfields, was abandoned for many years, a time capsule waiting to be discovered. Early visitors were astonished by the scene: the pyjamas still on the bed, the tea solidified in a cup, the A to Z marked up with a record of wanderings around London, the porridge on the stove, the weighing machine ticket shoved between the pages of a book, the notebooks full of ancient languages and mystical diagrams.

Photographers moved things around to create seductively spurious stage sets out of Rodinsky's junk. The room became an urban myth, "a museum of ephemera and dust-breath, a trap" (in Iain Sinclair's words) for a certain kind of romantic spirit. Yet who was this mysterious Vanishing Jew, this reclusive amateur scholar, simpleton or perhaps genius, and why had he suddenly disappeared in the late 1960s?

Rachel Lichtenstein knew all about such unfinished business. Growing up in a Polish village, her grandfather had shown a talent for drawing that led a rich uncle to arrange a place at art school. Arriving in Lodz, however, he was tormented by dreams so terrifying that he went straight home - and found his elder brother dead. He abandoned drawing forever, leaving it to his granddaughter.

Studying at Sheffield, she worked on sculptures based on his life and then began to research Jewish immigration from Eastern Europe to London. It was thus that she found herself in the former Princelet Street synagogue (planned to become a museum of immigrant life). She soon discovered that her grandparents had run a watchmaking shop only a few doors away and had probably been married there. But it was Rodinsky's room which began to obsess her. In investigating his shadowy existence, she has both untangled her own roots and created a marvellous elegy for an East End rapidly being engulfed in scaffolding, concrete and cappuccino bars, where only a single Jewish business - a funerary mason - is still thriving.

Lichtenstein's quest takes her to Israel, where she considers converting to Orthodox Judaism and is dissuaded by an amazing fortune-telling rabbi. Then to Poland as part of a Jewish tour where most of the participants are looking for traces of their ancestors and one hopes to find a treasure buried by his grandfather during the war. It is at Auschwitz that she realises her ultimate aim: to find out where Rodinsky is buried and grant his soul peace by reciting the Kaddish, the Jewish prayer for the dead.

This is a book touched with mystical notions, full of astonishing coincidences and lucky breaks (Lichtenstein spends weeks trying to contact an archivist in London and then runs into him by chance in a tiny Polish library). But it is also rooted in the hard slog of tracking down the old-timers besieged in their grim council flats who may have known Rodinsky, assessing their very contradictory memories and forging a coherent narrative from scattered hints. A cricket-playing "Ginger" Rodinsky turns out to be a false lead.

Perhaps the most memorable scene occurs in another former East End synagogue, taken over by an "art event" where two women "dressed in baby pink vinyl" picked up old books from a pile, stamped them with "large rubber implements" and tore the pages out. When Lichtenstein sees they are communal registers and important archival material, she screams blue murder.

This resonant account takes up almost two thirds of Rodinsky's Room and alternates with Iain Sinclair's far more wide-ranging speculations. These start rather wonderfully with an image of Lichtenstein, heavily pregnant, pitching the idea of the book to a New York literary agent. "So, you got 20 minutes," she is told. "A Frummer [religious Jew] in the attic, he disappears. Who should care? Where's the story?" Yet he soon becomes totally gripped: "In the film version you could freeze-frame the cigar smoke." Elsewhere, however, one gets a sense of Sinclair free-associating round the figure of Rodinsky, bringing in Pinter's Caretaker, the ghosts and golems of Prague, "locked room" detective novels, strange bohemian tricksters he has known, and his plans to write a book about a walk round the M25. Much of this is eloquent and illuminating, but the links do get rather tenuous.

Oddly enough, it was an article by Sinclair which Lichtenstein felt as a "prophetic warning" when she was just beginning her search for Rodinsky. The whole story, he had argued, was "a necessary selling point, to put alongside Nicholas Hawksmoor in the occult fabulation of the zone that the Eighties demanded to justify a vertiginous inflation in property values". This seems much too pat. It is a testimony to Lichtenstein's energy and empathy that she can make Rodinsky's drab, largely unnoticed life reveal far more than such an easy moral.