Stop to think for a moment and there is something very wrong about this one-off show from the Walkmen. They are a man down – bassist/keyboardist Walter Martin had to stay in the US with his pregnant wife – but, as singer Hamilton Leithauser confesses between songs, it hardly seems to matter. They start and end at the appointed times and their set is compiled with mechanistic precision, new songs sandwiching old, every shift in mood and tempo precisely modulated. Inevitably, they close with a furious thrash through their semi-hit, The Rat, so the audience can leave on a sing-along high.

This isn't rock'n'roll: this is professional musicianship. But the Walkmen have paid their wild dues, and have the stories of broken limbs and guitars to prove it. After 12 years and six albums together – the most recent, Heaven, was released last week – they sound settled, comfortable even.

What they don't sound is complacent. You don't stop to think, since they don't let you. From the moment guitarist Paul Maroon walks on stage and begins playing a shimmering, pensive waltz, they have you hooked. You can hear that melancholy waltz getting more refined as they dance through their back catalogue, from 2004's simple but affecting Hang On, Siobhan through the dense rumble of 2008's Donde esta la Playa. For all their peppy vigour – and in their sparkier moments, they still remind you of the Strokes – the Walkmen excel at a bruised, starry-eyed romanticism that draws its motifs from 1950s pop, with rockabilly trills on guitar, and knowing lyrical references ("I was a duke of earl," sings Leithauser on We Can't Be Beat). Stranded, another lilting waltz, illuminated with golden horns, earns their place in the timeline of classics.