Before Savages take to the stage, the Electric Ballroom is treated to as tuneless an intro tape as one could imagine: several minutes of churning bass noise, with what sounds like an electronic bell tolling through the aural drizzle. When they finally emerge, they stand in total darkness without playing, barely distinguishable silhouettes. So far, so doomy. It turns out not to be an act of artistic provocation: it's just their monitor engineer has gone missing. "I think we're fucking ready, all right?" announces singer Jehnny Beth, and they're off.

It's more than a decade since New York's "punk-funk" bands started co-opting post-punk into their music, but Savages have found the one corner of that music that hasn't been retooled by the millennial generation: the strident, declamatory end. At its worst – as on tonight's closing track, which Beth introduces with: "For every fucking fucker you met in your life … This is called Fuckers " – it's almost eye-rollingly asinine. At its best, though, it's as tart and refreshing as homemade lemonade.

Savages are at their best when they play fast. Guitarist Gemma Thompson uses her instrument mainly for texture and tone. On Flying to Berlin, half of the band's debut single from last year, it becomes apparent the song is divided into parts not by melody, but by sounds: Thompson's guitar chimes, then roars out for a chorus, then turns to PiLish screes of noise, then essays a surf-rock twangy lead line before returning to those original chimes. When the songs slow down, though, it becomes clear that Savages songs are only as good as Ayse Hassan's basslines: Thompson and Beth aren't melodicists enough, yet, to deliver thrills without velocity behind them.

Savages are indisputably a good thing: the world is hardly wallowing in unapologetically serious, all-woman bands at the moment. Especially not ones who have put so much thought into their aesthetic – have a look at the carefully filmed black-and-white live videos of them on YouTube for proof. They need to put as much thought into the music now: then the thrills will come thick and fast, rather than every so often.

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