Here is another example of a flourishing new literary genre: the theatrical revenge memoir. A couple of months ago we had Michael Blakemore's savagely compelling Stage Blood, in which the veteran director delivered the final and conclusive blow in his grudge fight with Peter Hall. Now, Croall, an admirably thorough, sensitive and industrious theatre biographer, is rehearsing his grievances against the late Sheridan Morley, a wayward, unreliable but enjoyably exuberant author, with whom he found himself in unwitting competition when both were attempting to write about John Gielgud. Croall's latest book, In Search of Gielgud: A Biographer's Tale, is an account of his attempts to get to grips with the ever-fascinating actor, then still alive. At the same time as capturing the challenges of trying to write about a living subject, its raison d'etre is the bizarre behaviour of the man he darkly refers to as The Other Biographer. The bizarre behaviour of Croall's publisher, Michael Earley of Methuen, who seems to do everything he can to avoid actually dealing with Croall or responding to his manuscript, provides a further subplot.

The central character in this saga is Croall, who presents himself as a mouse that roars – a solid, diligent, modest chap faced with behaviour that he will not put up with. It is initially a Pooterish self-portrait: he draws up lists, he writes memos to himself, gives himself monthly progress reports. He is delighted when Gielgud somewhat reluctantly agrees to allow him to go ahead with the book ("of course I cannot refuse my consent"), even though Morley had long ago secured the coveted title of authorised biographer. Croall is sceptical of Morley's ability to deliver a proper account of Gielgud's career: his earlier biographies of Coward, Gertrude Lawrence, James Mason, Dirk Bogarde and Morley's actor father, Robert, are peppered with inaccuracies and over-obsessed, Croall feels, with their subjects' private lives.

Croall sets out to interview as many people as possible, and he is taken aback by the strength of feeling of his ancient interviewees. Gielgud (right) occupied a unique position in the theatre of his time (and indeed in the theatre of our time). As Alec Guinness puts it to Croall, "he was the light of the theatre then." In a box of clippings and memorabilia at the Theatre Museum, Croall discovers a letter from an early idolater: "Twenty years ago your voice first entered my soul. If the bomb drops tomorrow and there is no God, the time has not been in vain, because you have moved and spoken." Gielgud lovers were mostly Olivier haters, and would often feel that way to the bitter end. Some of Morley's elderly interviewees are wonderfully indiscreet, joyously letting cats out of bags in which they have been confined for a lifetime. The 85-year-old Marius Goring, unable to recollect anything at all, suddenly remembers The Tempest, "which prompts him, in his dapper blue linen suit and white moccasin shoes, to execute a nimble little dance on the gravel. 'I was Ariel, and I danced like this in all the performances!'." As well as trekking round the dinosaurs of the profession, he finds the biographer's ignis fatuus: the unknown confidant, who has kept notes all his or her life. Croall's is Mavis Walker, oddly described as Gielgud's travelling companion; she has written an unpublished book about their jaunts together, and appears to have total recall of his conversation. "He once said to me, 'The thing to do with Shakespeare is to breast the waves, have the courage to let them take you, and don't think too much.'" It's sublime advice, and the key to Gielgud's incomparable art. Croall's progress report for July expresses great satisfaction, as well it might.

Then the Creature from the Black Lagoon stirs. Morley calls Croall's editor asserting his rights as authorised biographer. People he has interviewed are, he claims, bewildered about Croall. Next, Croall gets a letter from Richard Attenborough refusing to talk to him on the grounds that Gielgud has no knowledge of his book. "Am I in a dream? Can Gielgud actually have forgotten about the book?" he cries, and then, less gallantly, inquires: "Is this the onset of Alzheimer's?" Pooter now turns into a figure from Kafka, inhabiting a bewildering universe in which mysterious forces seem ranged against him. Morley is the most sinister of them, apparently removing files from archives, nobbling potential interviewees, poisoning publishers' minds; but his editor is equally incomprehensible in what he does and doesn't say. Gielgud himself comes to seem like an enemy, especially after Croall is again rebuffed, this time by the actor's old school. He decides to write directly to his subject: graciously but firmly, Gielgud asks him to stop writing, apologising for having wasted his time.

At this, Pooter becomes the Incred–ible Hulk. "Has he lost all touch with reality?", he asks his diary. "Oh, sorry, when you said go ahead, I assumed you meant it. How stupid of me. No of course I don't mind wasting a year of my life, just as I'm sure you wouldn't mind rehearsing King Lear for a year, only to be told that the production's off." When he calms down, he sensibly decides to carry on regardless, despite further rebuffs. Predictably, this drives Morley – who seems to have written very little so far, and has yet to interview Gielgud – to even greater heights of anxiety, rage and obstruction. Meanwhile, Gielgud himself edges closer to the grave. Croall persists in his struggle to see his subject calmly and clearly, instantly grasping the truth of how, as one interviewees tells him, "you felt and understood his pain, and that's what audiences loved. It was an extraordinary achievement for the least chameleon of actors. But maybe that's the thing, you always see John Gielgud, is vulnerability and fragility and spirit." And as these insights come Croall's way, Morley is issuing threats and denouncing the book as the equivalent of a Polaroid snap compared with the full portrait that he is painting. This remark naturally drives Croall close to insanity.

And so it goes on: insights, precious discoveries, threats, obstruction. Then, suddenly, Gielgud is dead, and what Croall calls the race to publication begins. He wins that, but Morley wins the battle for publicity; huge attention is paid to the authorised biography and, much to Croall's frustration, his own exhaustive and enlightening book – though not, as he himself admits, without its faults – is (as it happens, temporarily) eclipsed in favour of Morley's flashier effort. Croall mercilessly exposes his rival's errors of fact, tone and taste, and pursues Morley to the grave and beyond.

Revenge is, as Blakemore knows, a hard emotion to relinquish. Perhaps these writers feel that writing the books will free them of its vice-like grip. I wonder: closure is not so easily won. Croall seems not to be aware of the existence of But What Comes After?, the superb memoir written by Morley's widow, Ruth Leon, revealing the profound underlying instability of her late husband's personality. No comfort at the time, of course, but now … ? What transforms In Search of Gielgud are his startling illuminations of the great actor: who could have guessed that he visited Disneyland not once but six times? ("They've got a new Haunted House. Much better than their Pirates of the Caribbean") Or that he, of all people, would have reproached a company he was directing for being too English? The man, innocent and lyrical, lives in these pages.

• In Search of Gielgud: A Biographer's Tale by Jonathan Croall is published by Herbert Adler Publishing.