Within five minutes, a man's throat is nastily slit as he sits in the barber's chair and an underage pregnant girl streaming blood dies messily as her baby is delivered. Within 15 minutes, a dead body is found in a freezer and the fingers are cut off one by one to prevent identification before the remains are deposited in the Thames.

A few viewers may not survive this bloody onslaught but, this being a David Cronenberg thriller, however much you flinch, there's some point to the exercise. Besides, you wouldn't want to miss the superb sequence later on in which a naked Viggo Mortensen, towel discarded in Finsbury Baths, fights to the death against two thugs armed with curved Chechen knifes. More violence, but this time memorably choreographed like a particularly deadly ballet.

The film, set in a London not always recognisable, is about the Eastern European mafia, one of whom calls the town "the city of whores". Mortensen is the driver, ambitious with it, for a veteran Mr Big (Armin Mueller-Stahl) who runs a restaurant where the food looks delicious and where his avuncular charm holds sway. And he's got big by playing one gang of criminals against the other.

He also has a pathologically violent son (Vincent Cassel) who orders the driver about like a recalcitrant servant one minute and hugs him to his chest as a brother the next. Dad regrets his son's dangerous excesses, which include forcing the driver to have sex with one of the wretched girls in his brothel in order to prove he is not homosexual. The old man has, however, a secret of his own which may in the end prove his undoing.

The other leading character is an English midwife (Naomi Watts) working in a north London hospital who saves and looks after the dead girl's baby. She is determined, having found the young mother's diary, to find out who exploited her and who fathered the child, and becomes both fascinated and repelled by the flirtatious driver she meets along the way.

The acting throughout is excellent, particularly from a cold-eyed Mortensen who now and then suggests that he might be more human than we initially give him credit for. Watts has the enviable capacity of suggesting a normal woman rather than a star actor, trapped in the web of a concealed criminal-world that she only dimly understands. And those who remember Mueller-Stahl in Fassbinder films will know that, like Cassel, he is an actor of considerable subtlety.

This, though, is by no means Cronenberg's most intriguing or audacious film. Its subtext, which is about sex and violence and the way one often dovetails with the other, and the skill of its making, render it gripping enough. But it often seems no more than a clever pastiche of a Hollywood mafia movie set in London. There are also occasions when it looks as if quite a few minutes have been cut out of the story - either in the editing process or from the script.

Watch out for the fight in Finsbury Baths, however - it must have taken endless rehearsal to perfect and will probably come to be regarded as a classic cinema sequence.