Twenty years ago, Neil Jordan's film Interview With The Vampire was a sexy and provocative shot in the arm for the vampire genre.

Since then we've had Twilight, True Blood, The Vampire Diaries, Let Me In, Underworld, Dark Shadows – teen vampires, lovesick vampires, socially integrated vampires, action hero and comedy vampires. Just when the genre seemed sucked dry, Jordan returns to replenish it.

The central dynamic of Interview was a twisted vampire "family" involving a homoerotic Brad Pitt and Tom Cruise and their surrogate daughter, a child forever trapped in a body that little suited her hungry disposition. There's a family foundation in Byzantium too, though this time the unit is more conventional, namely a mother and daughter. That said, one is in her early twenties, the other 16, fixed in time at such similar ages that they could be sisters. Theirs is a unique parent-teen conflict which they've had to deal with for two centuries.

Nor are Clara (Gemma Arterton) and daughter Eleanor (Saoirse Ronan) ordinary vampires: they can exist in daylight and don't have fangs, instead cutting their victims open with a chillingly reactive thumbnail. They're also less glamorous than we're used to. While Clara is lap-dancing to pay the rent, Eleanor mopes around a dingy estate, writing the story of their lives, only to toss it away when it's finished and start over – mum's house rule being that if anyone happens to read it, they must die. The pair may be bonded by blood, but are chalk and cheese: Clara brassy, no-nonsense, instinctive, choosing to feed off assorted misogynists; Eleanor melancholy, reserved, only killing people who are already dying or wish to.

A brilliant scene-setter sees a semi-clad Clara chased from her sex joint by a powerful man, a tracking camera thrillingly following them through busy streets and into a shopping mall. It's a little reminiscent of Harrison Ford's pursuit of the snake-charming android in Blade Runner, though this time the conclusion is, spectacularly, in the woman's favour. Nevertheless, the vampires must now relocate to a down-at-heel seaside town, where Clara sets up a brothel in a former guest house known as Byzantium, and Eleanor joins a new school, her urge to let her history be known growing ever stronger.

Eleanor's prose provides a back story set in the early 1800s that explains how she and Clara became vampires, and why a glum bunch of male vampires, the Brotherhood, is hunting them down. Jordan takes us back and forth in time, giving us two stories for the price of one – a Gothic tale introducing a vampire lore different to anything we've seen, and a baroque contemporary thriller. The whole thing drips with atmosphere – vibrantly photographed, the locations brought vividly to life, the violence suitably shocking.

Interestingly, both Jordan's vampire films have been written by women – Anne Rice adapting her novel for Interview, Moira Buffini penning an original screenplay for Byzantium – lending a female perspective on a genre dominated by men. Buffini posits her female vampires as the chief protagonists, men trailing in their wake.

Johnny Lee Miller, as a syphilis-ravaged rogue, and Sam Riley as an enigmatic member of the Brotherhood are the best of those male combatants, but the film belongs to Arterton and Ronan, who bring very different energies and acting styles – respectively, in-your-face and introspective – to bear on their dysfunctional kinship.

Around them Jordan lends this vampire story the air of a fevered fairytale. Some of it is daft as a brush, but this director likes to push boundaries, and is invariably good enough to get away with it.