Bon Iver, Victoria Apollo, London

One man's pain becomes pleasure for thousands

This is an extremely big deal for us," says Justin Vernon, standing beneath a giant pterodactyl. Vernon is the songwriter, lead singer and creative mainspring of Bon Iver – indeed, to all intents and purposes he is Bon Iver, whose melancholy masterpiece For Emma, Forever Ago was one of the year's happiest surprises.

A word-of-mouth success since its release in May, For Emma, Forever Ago is, as the title suggests, a break-up album, albeit a break-up album with a difference, Vernon having recorded it entirely alone in a snowbound log cabin in Wisconsin, where according to the rapidly growing legend, he cut logs and hunted deer to survive, while overdubbing the torment out of his system in lonely recording sessions. At the time, he can have had no idea whether what he was doing was any good, or whether the months of cabin-fever had destroyed his judgement, and he was simply unspooling obsessively about stuff nobody else would be interested in.

A year later, there's no doubt about the resonance of his personal turmoil. Tonight, for instance, there are 2,400 people in a sold-out London theatre hanging on Vernon's every word as he and three friends bring the frosty solitude of his songs to life. Like many an American outsider artist before him, Bon Iver has found his warmest welcome in the hearts of Europeans, particularly Brits, with For Emma, Forever Ago vying with Fleet Foxes's self-titled debut for the position of American indie album of the year.

The two acts, as it happens, are not that dissimilar in approach, both employing a sort of 21st-century rustic moderne sound overlaid with gorgeous falsetto harmonies that recall both the great Seventies country-rock icons (Byrds, CS&N, Eagles) and the harmony vocal tradition's roots in religious music. Vernon's original layered harmonies are rendered live by all four of his band, which includes – surprisingly, given the introspective nature of his songs – two drummers. Both, however, have second and sometimes third instrumental duties, switching between bass, guitar and keyboards, while second guitarist Mike Noyce sits stage left, adding tints and shades to Vernon's gently-strummed odes.

Around the band looms the stage-set for the musical Wicked, the theatre's day-job. It's a weird contrast of moods, but the musical's lighting effects complement the haunted nature of Bon Iver's songs, casting spooky backdrops of swirling blue on to the circular screen behind the band. The set opens with him chanting the lines "I'm out in the woods, I'm down on my mind/I'm building a still to slow down the time" over and over. Gradually, the other players join in the chant until the lyric becomes a sort of bucolic mantra.

It's followed by the album-opener "Flume", all four musicians crooning in ghostly unison falsetto until the gentle, folksy arrangement suddenly collapses in on itself in a burst of free-form avant-rock. "Skinny Love", the first single from the album, is accompanied just by loud chords from Vernon's rusty-brown resophonic guitar, until all three of his bandmates add a brutal drum stomp; as elsewhere in the set, there's a weird, gospel edge to the call-and-response vocals, with Vernon's falsetto lead answered by another loud unison chant. During "For Emma", the audience is also encouraged to keen along with the band – as sinister a sound as any the theatre might experience during its weekly delvings into witchcraft.

The wonderful album closer "re: stacks" is delivered solo by Vernon, his high vocal lines ringing around the theatre like the lament of a lapsed choirboy, before the audience is again cajoled into another community singalong for the set-closing "Wolves". One of several new songs from the forthcoming Blood Bank EP, "Babies", provides the first of two encores. "It's a happy song," observes Vernon, keenly aware of how contrary to his usual mood this is.

It's not as hermetic and singular as the songs from Vernon's months of solitude, reflecting perhaps the hubbub of activity around a new-born child. Whether he and his band can bring a similar magic to this new, crowded mode as he did to the isolation of For Emma, Forever Ago remains to be heard. For the moment, they're the favourite band of at least 2,400 enchanted fans.