Did Graham Greene invent film noir? I've always secretly hoped the answer was yes. It would be fitting that Britain's miserable, morally conflicted poet of the third-class railway compartment could be established as the prime mover behind the darkest, nastiest and sourest cinematic style of all - rather than bullish American wordsmiths of the James M Cain and Dashiell Hammett stable. We all know Greene had a hand in arguably the finest noir ever made, The Third Man, and the adaptations of Ministry of Fear, Brighton Rock and The Basement Room (known in cinemas as The Fallen Idol) are all noir classics of one kind or another. But they were all a little late to the film-noir party, reaching cinemas between 1944 and 1949.

A much better claim can be staked by the 1942 film This Gun for Hire, adapted — very loosely — from Greene's 1936 novel A Gun for Sale. In its page-to-screen trajectory, This Gun for Hire exactly resembles, and predates, James M Cain's Double Indemnity, the film of which came out in 1944. You can theorise that the novelists, generally writing before the second world war broke out, sensed the slide to conflict well before the considerably more conservative film industry. Or maybe they were just smarter. Whatever the reason, A Gun for Sale made a great noir source, even if the resulting film does a fairly radical job on Greene's original. Unsmiling hitman Alan Ladd is a long way from the novel's hare-lipped and twitchy Raven, while nightclub canary Veronica Lake vamps at levels unknown to Greene's danseuse Anne. And the yards of ultra hardboiled dialogue, courtesy of The Naked City's Albert Maltz and The Asphalt Jungle's WR Burnett, turn it into down-and-dirty American pulp.

Early though This Gun for Hire is in the noir canon, it's still later than The Maltese Falcon, Suspicion and even Stranger on the Third Floor — the 1940 Peter Lorre vehicle normally considered the first of the classic American noir phase. But Greene has a much earlier claim to noir fame; he wrote an original script for a British crime thriller called The Green Cockatoo, which was released in 1937. The Green Cockatoo is one of those oft-mentioned, hardly-ever screened films, and the only way you can get to see it at the moment is to request it from the National Film Archive - which is exactly what I did.

So is The Green Cockatoo actually any good - and equally importantly, is it a genuine film noir? The answers are: sort of, and maybe. Roughly contemporaneous to A Gun for Sale, Cockatoo has a similar commitment to the boiled-down essentials of the crime genre. A girl witnesses a murder, becomes a suspect herself, falls in with a Soho tough-nut (John Mills, doing the worst American accent this side of Vivien Leigh), and eventually realises he's the murdered man's brother. Being a film, and a pretty fast-and-cheap one at that, much of the layered detail that Greene inserts into his prose is lost, so in many ways Cockatoo comes across as a pretty rudimentary entertainment. On the other hand, some unmistakable Greene touches shine out — the girl, for example, is described as wearing a "cheap white mackintosh", a fantastically redolent phrase that instantly puts you in that fabled Greene-land. Alongside that, he hints at some interesting themes — the divided self, the moral crusader, the labyrinth of the city — that would become noir staples. That said, it's all topped off with a cheesy kiss in a railway compartment that belongs in a sappy romance.

So it's perhaps understandable that The Green Cockatoo isn't numbered in the front ranks of noir, but Greene deserves points for trying. There's a direct line to later spivs-in-Soho films like Night and the City and The Small World of Sammy Lee, and therefore it's well worth cherishing.