Consider the strange and remarkable case of JK Rowling. Her first book, for children, Harry Potter and the Philosopher's Stone, was rejected by at least 12 publishers. It was bought for £2,500 and published, in 1997, in an edition of about 1,000 copies.

Rowling's storytelling struck an immediate chord with juvenile readers. Within a year, she was winning all the children's book prizes. By the time two Harry Potter sequels – The Chamber of Secrets (1998) and The Prisoner of Azkaban (1999) – had been launched, Rowling was a pawn turned queen, and her work a global cult.

Not since Arthur Conan Doyle's Sherlock Holmes stories had a writer of Scots ancestry – indeed, any writer – achieved such an astounding audience. Subsequent Harry Potter adventures smashed all known sales records. In 2004, Forbes magazine named Rowling the first person to become a billion-dollar author.

Just as remarkable, in 2007, Rowling completed her seven-volume Harry Potter sequence, with The Deathly Hallows, nailing down almost every last detail of a mind-bendingly intricate plot, and bringing an elephantine narrative to a satisfying and possibly open-ended conclusion. In the annals of British literature, Rowling's Harry Potter series is an unprecedented achievement.

Inevitably, there was a reckoning. In 2011, after a troubled hiatus, Rowling fired her agent and the following year published The Casual Vacancy, a novel for adults, under her own name. The reviews were mixed, but she still sold more than a million copies worldwide, while clearly relishing this second act in her literary career.

Meanwhile, like Conan Doyle, who followed Holmes and Watson with his Professor Challenger novels, Rowling hankered for another series. Unlike him, she wanted to write and publish without the hype or expectation surrounding her literary life. Secretly, she adopted a pseudonym and forged a new protagonist. Once again, the author of Harry Potter was in the business of creating an alternative world for herself. She almost got away with it.

Almost, but not quite. When, in April 2013, Little Brown published a debut crime novel by a certain Robert Galbraith, described as "a former plainclothes Royal Military Police investigator", there was a smattering of excellent reviews, the usual modest sales (some 1,500 copies) and then… Hey presto! Rowling's secret was out. She was "Robert Galbraith".

Sure enough, The Cuckoo's Calling became a No 1 bestseller. Whatever Rowling's aspirations to control the execution and reception of her mid-career progress after Harry Potter, the awkward truth is that she is now the rich-and-famous victim of her celebrity, with all the consequent stresses of such a fate. Intriguingly, her second Robert Galbraith novel is a playful, obsessive yarn about the ironies of the literary life.

Novelist Owen Quine goes missing having just completed a manuscript replete with vicious pen-portraits of his nearest and dearest. In the works of Conan Doyle's contemporary, PG Wodehouse, such a premise is the basis for farce. Not here. Tellingly, for Rowling, Quine's literary evisceration of his agent, his editor, and his publisher forms the basis for a detective story that does not merely suspend disbelief but hoists it like an escape artist over an abyss of improbabilities.

Private detective Cormoran Strike (named after a mythological Cornish giant) is commissioned by Quine's wife to track him down and bring him home. After 123 pages of teasing stuff about literary London, revenge tragedy and the Latin for silkworm (Bombyx Mori), Strike finds Quine horribly murdered (trussed, eviscerated, and putrid) in an empty house, 179 Talgarth Road, W14. There is no shortage of nasty suspects with creepy hidden drives, ample opportunity and oodles of motive. Now read on....

But this, disappointingly, is where the trouble starts. The Silkworm labours hard to be silky, but English prose has never been JK Rowling's friend and she herself betrays a tell-tale anxiety about her project. There's a revealing moment on page 166 at which, in the guise of a fictional blog, she instructs the reader in the difference between plot and narrative. "Plot is what happens," she writes. "Narrative is how much you show your readers and how you show it to them." In Rowling's imaginative landscape, then, there is no serious consideration either of character or situation. To these two novelistic essentials she is a stranger. Indeed, the dog that never barks in this "narrative" is any character you could identify with, or even understand.

One clue to this absence lies with Harry Potter. A gallery of grotesques challenged by an everyman (or every-boy) was Rowling's formula. The "death" that was a major subtext in Hogwarts becomes explicit in the real world of Cormoran Strike. But without characters the reader can relate to, we're back with the old problem. How to make a narrative out of a plot, and worse, how to make a thriller out of a situation that is intrinsically comic?

Rowling's answer to this conundrum is to bamboozle the reader with what her blurb calls "twists at every turn". Plot, however, is not enough. What diverted millions in Harry Potter now becomes one damn thing after another. Indeed, the exposure of the killer comes as an anti-climactic relief. Rowling tells us that silk was extracted from silkworms by boiling them alive. Inside this overwrought cocoon, there is perhaps some magic, but the necessary sacrifices of art are never part of renewing global bestsellerdom.

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