London Grammar are a classic case of rose-without-trace. A year ago, the three young Londoners hadn't released a note of music; today, their CV includes a No 2 album, If You Wait, and the attentions of the Radio 1 Breakfast Show, which tweeted that singer Hannah Reid was "fit". The ensuing Twitter backlash brought them on to the mainstream radar, but they would have got there eventually, DJ Nick Grimshaw or no – this is a group whose woebegone indie shop-window conceals a warehouseful of potential hits.

Reid, guitarist Dan Rothman and synthist Dot Major (whose double-take resemblance to Harry Styles of One Direction doesn't go unnoticed by a quartet of partying Brighton females) have just returned from their first US tour, a fortnight apparently so unsettling that Rothman's only comment tonight is: "We're really glad to be home." You can only imagine what happened – one thing American hipsters love is an unfathomable English band, and in London Grammar they had the full brooding-Brit experience.

At 23, Reid is already capable of transfixing a room: from the first chilly ululations of the opening Hey Now, the crowd fall silent. Rothman and Major create patterns of swooshes and drones that morph into Portisheadish trippiness on Stay Awake With Me and – it must be said – Sade-style lounge-rock on Flickers. It's a recipe that works especially well onstage, where blue lighting bumps up the haunted-house feel and illuminates Reid, standing eerily composed and separate from other band members.

Frequently, all this coalesces into oddly hummable tunes that have already been adopted by fans as angsty anthems. Strong and Wasting My Young Years are tonight's tours de force, with the emphasis on "force": the crowd relate to these diary-style outpourings of early-20s uncertainty, but even more so because they're driven by Reid's most impassioned delivery. Promising? You could say so.

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