Book review: The Cuckoo's Calling, By Robert Galbraith (AKA JK Rowling)

It's probably best, for the moment, to forget Robert Galbraith's real identity; this is a very good book in its own right.

Get money off this title at the Independent's book shop

If it was turned down by other publishers who had no idea of who the author was, that is as much a criticism of the constraints under which modern editors work as of the book itself. It is a classic detective story which takes its time to get where it is going because its detective is a systematic investigator doing due diligence. The mapping of one witness's story over the next, the search for inconsistencies and alternative explanations, makes for a leisurely read and a lot of pages – but there is almost nothing here that can be described as redundant.

Cormoran Strike, one-legged bastard of a rock star, military policeman turned private eye, is not doing very well in his new career. He has finally broken up with his long-term, on-off, lover and is sleeping on a camp bed in his office; he thinks much of this is other than obvious to Robin, his new temp.

Hired by her brother John to investigate the apparent suicide of supermodel Lula, Strike almost doesn't take what looks like an open-and-shut case; the woman was troubled, had a bad relationship, was alone when she fell from a balcony into the street. One of the serious strengths of this book is that it does not insult the intelligence of the police who, it gradually turns out, got things wrong – this is a book, amusingly in the circumstances, about how we see what we think we are going to see.

It is a book about looking and listening – “The dead could only speak through the mouths of those left behind and through the signs they left”. Cormoran, and Robin as she becomes invested in his work, spend time in Lula's world – rappers, actors, designers and lawyers. Cormoran, who has only met his famous father twice, finds himself moving in a world where he feels like a fish out of water, but is thought of by its denizens as belonging. There are some touches here of very sardonic social comedy, interestingly reminiscent of Margery Allingham's classic The Fashion in Shrouds. Allingham's snobbery, though, is mostly missing – not entirely, since Lula's working-class birth mother is something of a Daily Mail caricature.

There is an intelligent ear here – the speech rhythms are caught convincingly enough that we don't need the occasional descent into phonetic spelling. Galbraith is generous in sometimes surprising ways; Lula's obnoxious, vaguely abusive boyfriend turns out to be a more complex character than we and Cormoran at first assume.

It's also a book about using loss to develop emotional intelligence, and about friendship. Cormoran learns to care whether Lula killed herself, from her friends, and at the same time builds a relationship of trust with his new temp. Cormoran has been damaged by a romantic obsession and his inability to save his drug-addicted mother; Robin, who has a fiancé already and is fascinated by his work, is the equal female friend he precisely needs. If, as a result of the revelation that Galbraith is JK Rowling, this is the first of a series, that is good news.

Roz Kaveney's books include Superheroes! Capes and crusaders in comics and films (IB Tauris)

The Cuckoo's Calling By Robert Galbraith Sphere, £16.99. Order at a discount from the Independent's book shop