"We don't want to be stuck playing Hackney every Friday. We exist outside all that," Cat's Eyes singer Faris Badwan said recently. Indeed, the debut London show of this Anglo-Canadian duo took place not in the capital's hipster east but a deconsecrated chapel in west London. Badwan, frontman of the Horrors, and Rachel Zeffira, a Vancouver-bred musician, may look overwhelmingly "Hackney" in their disheveled black hair and tight black clothes. But their sound is some way removed from the indie-guitar template.

They do employ alt-rock touchstones. Over the course of 35 minutes, Cat's Eyes stir up the spirits of Cowboy Junkies, My Bloody Valentine (who had a big effect on the Horrors' last album), and, when Badwan and Zeffira combine voices, Nancy Sinatra and Lee Hazlewood. Backed by guitars and drums under a screen showing fragments of black-and-white films, they are not reinventing the wheel, but are inarguably striking.

The first few songs, which include a Pink Floyd cover, Lucifer Sam, do not have what you would call structure; instead, they derive their clout from the ethereal sighs of Zeffira and a backing vocalist. During The Best Person I Know, a shoegazing throwback of organ and vocal, the backing singer literally stares at her footwear. Are Badwan's eyes glazing over? No – he is readying himself for the distortion-pop assault of Face in the Crowd, which gives listeners a resounding thwack in the head. Then the delicate I'm Not Stupid delivers a lovely surprise: a female choir appear in the balcony to add feathery harmonies.

Despite the drifty troughs, there are enough peaks here to make Cat's Eyes a side project worth listening out for.