The murder of Allan Chappelow in Hampstead in 2006 was widely covered not just because the victim was decidedly eccentric and vaguely famous, having written books on George Bernard Shaw. The case also became notorious because the murder trial was partly held in camera, meaning the press and public were excluded for reasons of national security (the accused was a well-connected Walter Mitty type from China). Thomas Harding grew up only a few doors down from Chappelow, so his is a first-person investigation of the murder, of police procedure, of the British establishment and, even, of human nature.

Chappelow was the son of a Danish mother and an authoritarian Englishman. He studied moral sciences at Trinity College, Cambridge. From a long line of conscientious objectors, he found service on the home front in the second world war, first on a farm, then as an air-raid warden. He became a photographer and writer, meeting HG Wells, Somerset Maugham, Augustus John and Bertrand Russell. He was, Harding speculates, probably gay, and possibly a habitué of the nearby heath. In the last decades of his life, he lived in near squalor in his old family home in Hampstead. He rarely seemed to wash and was increasingly vague, deliberately isolating himself.

Wang Yam was very different. He had had a tough, itinerant life in China. He claimed to be the grandson of one of Mao’s most famous revolutionaries, though this – like most of his life story – is disputed. He was on the fringes of the Tiananmen Square protests, before seeking asylum in Britain in the early 1990s. He set up businesses with abandon, although his cheques invariably bounced and he eventually went bankrupt. His personal life, too, was messy: he and his first wife divorced, he had a fling with a Chinese woman called “Jenny”, and then met another woman who was, by 2006, pregnant. That summer he was desperate for money but prone to asking estate agents to show him round multimillion-pound houses in London.

The case against Yam was that he had stolen Chappelow’s post and identity, emptying his savings and passing them on to “Jenny” before fleeing to Switzerland with his pregnant girlfriend. No forensic evidence linking Yam to the Hampstead house – where the victim was discovered under half a tonne of papers – was ever found. Over the course of the book, it becomes clear that Harding is unconvinced of Yam’s guilt, and is increasingly bewildered by the certainties of the police and the prosecution.

Structurally the book is both refined and slightly peculiar. It splices the backstories of the victim and the perpetrator, and weaves into those two narratives the police’s investigation, giving the book a truly satisfying geometry: for a few pages you’re with Chappelow in the 1930s, then in 1960s China with Wang Yam, then in north London in 2006 as the police try and make progress in their investigation. The collision of those distant worlds is eerie but compelling.

But just as the narrative drive threatens to hit fifth gear, there are little italicised chapters called “Case Notes”, which are first-person descriptions of the writer’s travails: his struggles with establishment bureaucracy, evasive relatives and the phone calls and fantasies of Wang Yam. Rather odd to begin with, these asides actually grew on me: some might enjoy that peep behind the wizard’s curtain, or relish that postmodern framing of the narrative, but purists of the true crime genre might just find it irksome.

The last quarter of the book gets bogged down in the minutiae of (post-trial) legal processes, meaning that the story peters out rather than climaxes. Legal drama is, after all, invariably a contradiction in terms. There’s an epilogue and a postscript. Maybe I’m old-fashioned, but there are more split infinitives than unsplit ones.

But it’s a fine and fascinating read, bolstered by exemplary research and nuanced insights. It’s absorbing and melancholy precisely because there’s a strange symmetry to the main characters’ lives: one lived in the same home almost all his life, while the other was a rootless drifter who had never had a home. The murder was a clash between an old man who cared nothing for, and a younger man who was nothing but, appearances.

• Blood on the Page by Thomas Harding is published by William Heinemann (£20). To order a copy for £17 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99