Directed by Guy Ritchie. Starring Robert Downey Jr, Jude Law, Rachel McAdams, Mark Strong, Eddie Marsan, Kelly Reilly 12A cert, gen release, 128 min

HERE’S A thought. According to Professor Internet, more than 70 actors have played Sherlock Holmes in some 200 films. Yet it has been nearly 80 years since a major theatrical release actually bore the title Sherlock Holmes.

We've had our Sherlock Holmes and the Voice of Terror. We've thrilled to Sherlock Holmes and the Secret Weapon. But the name alone, unaccompanied by adversaries or references to a Conan Doyle story, has failed to interest the industry's enablers.

The starkness of the new film's name has troubled Holmes purists. You expect to see this sort of thing on the poster for a superhero film – Spider-Man, Batman, Iron Man– but the great Victorian detective does not normally rub up against such vulgarity. Baker Street Irregulars were further troubled by the intelligence that Guy Ritchie, Lord Mockney of Lock-Stock, was to direct the picture and Robert Downey Jr, Iron Man himself, was to play Holmes. Forget about it. They may as well have called the thing "Holmes-Man".

Well, there is plenty here to further annoy the faithful. Within the first 10 minutes, we encounter Holmes, stripped to the waist, engaging in a bare-knuckle boxing match. Exhibiting all the twitchy mania we expect from a Robert Downey Jr character, he also leaps across yawning cavities, discharges guns every five minutes and – steady there, Mrs Hudson – exhibits a jealous affection for Jude Law’s Dr Watson that borders on the homoerotic. (Moreover, he hits his consonants with weirdly unnatural fervour, but that is, surely, down to Downey Jr’s difficulty with the accent, rather than any creative revelation.)

Yet, for all its irreverence, this Sherlock Holmes proves to be an absolute hoot. Closer in tone to near-contemporary melodramas by the likes of Sax Rohmer and H Rider Haggard than to Arthur Conan Doyle's imperishable mystery stories, the picture packs every frame with delirious activity and never allows the pace to slacken. After deranged missteps such as Revolverand partial successes such as RocknRolla, Ritchie appears to be right back in the hunt.

What’s it about? You may as well try and summarise a weather system. We begin with Holmes and Watson discovering the insanely villainous Lord Blackwood (Ritchie regular Mark Strong) engaging in what appears to be an act of unspeakable black magic. Unfazed by his wretchedness, they apprehend him and turn him over to the reliable Inspector Lestrade (Eddie Marsan, born for the role). But what is this? Days after his hanging, Blackwood rises from the grave and – now revealed as a hideous combination of Aleister Crowley and Oswald Mosley – begins planning a new world order.

Not much at home to narrative order, Sherlock Holmessucceeds on texture, tone, ambience and sheer, unrelenting busy-ness. Although it never looks anything other than a computer-generated environment, the film's vision of London is as disgustingly filthy as it is intriguingly fecund: a half-built Tower Bridge looms, the river teems with jockeying vessels, Baker Street's white buildings are smeared with soot. This is also an unexpectedly Irish version of the city. The likes of Bronagh Gallagher and Ned Dennehy lurk with Hibernian menace and Hans Zwimmer's score – his best for a decade – punctuates its carnival revels with jaunty jigs and reels.

None of this is to suggest that the picture is anything other than high-grade pulp. Downey Jr may bring a classy kind of madness to his Holmes, but the character remains a cartoon and the story plays to the beats of a penny dreadful. It is, however, an achievement when such an entertainment’s cliffhanger gestures genuinely leave the viewer wanting more. Come to think of it, there’s never been a film called “Sherlock Holmes 2”.