By all accounts, the Australian Nobel laureate Patrick White, who died in 1990, was one of the most contrary and difficult writers ever to set pen to paper.

Best known perhaps for his 1957 novel Voss, which became a bestseller and made him famous, White did his utmost to keep the world at bay. He gave few interviews, refused almost all honours, spoke rarely in public, did not turn up to accept prizes and had a Sicilian capacity to pursue feuds.

But much as he hated other people, it was nothing compared to his self-loathing. As David Marr, his excellent biographer, has remarked, "Terrible as he could be to others, he was worse on himself. There were times he seemed to be a man at war, the victim of a battle always going on within himself."

Among the "diseases" with which White believed he was afflicted were those of memory, which did not allow him to forget slights, and writing, which gave him no rest. On his death, the obituaries were mixed. The same was true of the reception much of his work received when he was alive, even in his native country.

Nevertheless, White is – with the possible exception of Peter Carey – Australia's greatest ever novelist. Stylistically, he could be opaque and his essays into stream of consciousness, a la Virginia Woolf, were not always successful. But there was evidence on every page he wrote that he was a writer of natural and distinctive gifts, brilliant at bringing together people from disparate backgrounds and fusing their experience into something memorable, significant and enduring.

I have long been an admirer of his. Recently, I pulled from the shelf a copy of Riders Of The Chariot, bought secondhand, and found in it a thank-you letter in which the original recipient of the novel – an English schoolmaster – communicates his joy at reading it and its "moving and profound and convincing" story of a Jew who has escaped the gas chambers. That is a typical reaction among White devotees, of whom there are far too few.

The manuscript of The Hanging Garden was found on White's desk after he died. As David Marr explains in an afterword, he had insisted that all unpublished manuscripts be destroyed. Persuaded that White himself would have destroyed it if that's what he really intended, White's literary executor, Barbara Mobbs, agreed to allow this fragment, reckoned to be about a third of the projected whole, to be published.

More often than not this is not a wise decision. Literary history is replete with unfinished novels which ought never to have seen the light of day. Happily, this is not the case with The Hanging Garden, with its Babylonian overtones. Rather, the feeling that remains after reading its 200-plus generously spaced pages is one of regret and sadness at its incompletion.

What is instantly apparent is White's mastery of his art. He does what so many other writers ought to be able to do easily but often can't, which is set a scene economically and vividly. The era is the second world war, the location the shores of Sydney Harbour. A boy, Gil, and a girl, Eirene, are thrown together in the home of a Mrs Bulpit. Both Gilbert and Eirene have lost a parent. Gilbert's mother died in the London Blitz; Eirene's father, a Communist, was executed in a Greek prison. The novel opens with the delivery to Mrs Bulpit of Eirene by her mother, who must return to war-torn Europe.

Every detail, every conversation, is freighted with meaning. "My husband was a Greek – a Greek patriot," Eirene's mother, who has "the figure of a dressmaker's dummy", tells Mrs Bulpit. "And I was Australian before I married. I do not think of myself as British." Mrs Bulpit is characterised with Dickensian boldness. She is pale, except for her "painted" lips. "Her forearms, hands, and face could have been moulded from natural marzipan." She is a stickler for correct grammar and says of Eirene's Greek genes, "I'm not all that gone on foreigners, but she's a human being, isn't she?" Her house, meanwhile, "smells of mushrooms and dust".

Gilbert has arrived in Australia by way of America where he was in the care of clergy. His father is in India. Like many of White's characters he is a refugee, seeking safety. In the Blitz, his friend Nigel died, as did an aunt and the woman at the corner shop. "You could believe in the deaths of older people," Gil thinks, "but not of Nigel, any more than yourself could die."

Gil and Eirene have to abandon their pasts but this is easier said than done. For them, as for so many others during the war, the past is cruelly present. But they are children, and growing up dominates daily life. White himself was an expatriate, sent to England to be educated, which made his future relationship with Australia uncomfortable to say the least. He was also, in that most macho of cultures, homosexual, living for decades with his Greek partner. It created a sense of alienation which he imported to his fiction, to which The Hanging Tree, incomplete as it may, is a haunting and tantalising postscript.

The Hanging Garden

Patrick White, Jonathan Cape, £14.99