The Walkmen, Shepherd's Bush Empire, London

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From Long John Baldry to Jarvis Cocker, beanpole pop stars seem to inspire a special kind of affection, and from the sensational performance he gave here, Hamilton Leithauser is worthy of being – as it were – right up there with them.

Leithauser is the frontman of New York band The Walkmen, and he is extraordinary in more ways than one. Let's deal with the superficial stuff first. So there's his height, which is considerable – around 6ft 4in. And there's his dress sense, which recalls a 1970s-era clothing catalogue aimed at the groovy man about town. Indeed, the last time anyone took to the stage looking as Leithauser did – polished brogues, smart trousers, an open-neck shirt, a brown sports jacket, conservative haircut – it might have been Long John Baldry himself.

Finally, there are Leithauser's contorted movements – the crooking of an elbow, the standing on one leg while the other twists off at improbable angles – which give physical expression to the mixture of joy and anguish characteristic of so many of The Walkmen's songs.

If this music has to be called indie, then it's very much indie for grown-ups, and the real point about Leithauser is that he possesses artistry of tremendous power and eloquence, and his tenor croon – which can do both gravelly and ethereal – sends tingles down your spine. Blend Bob Dylan with Neil Diamond and you wouldn't be far off.

The band formed in 2000 and have released six albums, of which their most recent, 2010's Lisbon, represents their finest flowering. Bafflingly absent from many of the year's best-of lists, Lisbon is a series of dispatches from love's front line, where victories are hard won, pain is a constant, rejection inevitable. But there's nothing mawkish about The Walkmen. A strain of bruised optimism runs through everything they do. Even when their layers of sound reach Spector-ish levels they retain a wonderful lightness of touch, perfectly balancing intimacy with grandeur, and the listener is invited to bathe in a warm lagoon of jangly guitars and skipping drum-beats. The Walkmen craft a thoroughly contemporary sound from impeccably vintage instrumentation.

That they were less shambling on stage than they are on record was in large part due to the precision work of lead guitarist Paul Maroon and keyboard player Walter Martin. But they established their cathartic credentials early on with the blistering "Angela Surf City", and it was soon clear why Guy Garvey has described The Walkmen as the best live band he's ever seen.

"Blue As Your Blood" took a Johnny Cash rhythm and laid a dreamy melody on top; the lilting swamp rock of "Canadian Girl" owed something to The Jesus and Mary Chain (not to mention all the people the Reid brothers were indebted to); and "Juveniles" just sidled up and opened its heart. The exquisitely graceful "While I Shovel the Snow" was Leithauser at his virtuoso best – a captivating display of controlled emotion with only a simple tune picked out on Maroon's guitar for accompaniment.

Patti Smith was in town the same night as The Walkmen were playing. Sometimes one can be spoilt for New York legends.