Bon Iver, Hyde Park, London

The back story that accompanied Bon Iver's debut album For Emma, Forever Ago has already made the 28-year-old star from Wisconsin a legend in contemporary folk-rock. After a relationship breakdown, Justin Vernon retreated to his father's log cabin in wintry Wisconsin for three months, killing deer to feed himself, and in seclusion wrote the record that topped critics' lists of albums of last year.

Like its secluded conception, it's an album of loneliness, to be listened to alone with your thoughts. It was certainly not created for thousands of fans to sing along to in Hyde Park. But on one of the hottest days of the year and the second evening of the outdoor concert series, the Serpentine Sessions, an intimate space suited to the mini folk-rock festival it is hosting, has been set up. Outside the main tent on another smaller stage, rising star Beth Jeans Houghton, a 19-year-old from Newcastle, plays trumpet-lifted folk songs. Best of all is the selection of another of folk's fastest-rising talents, Alela Diane, watched by Bon Iver from the wings. Fingers gliding over acoustic guitar, joined by her father on mandolin and electric guitar, "White as Diamonds" from her recent beguiling album, To Be Still, shimmers in a short set that points to an expansive future.

For the fans gathered here today, it is a rare sighting of Bon Iver. Those expecting a man looking like he's emerged from the wilderness are half right. While Vernon's beard is in check, his wispy golden hair has certainly grown and sprouts up – and outwards. When he plays the most gut-wrenching of his songs of heartbreak, the psychedelic tendencies of his music are brought to the fore. "Bracket, WI", the song he contributed to Aaron and Bryce Dressner of the National's compilation album Dark Was the Night, with the aid of three bandmates, builds up eerie organ effects on synth and guitar in the vein of "It's A Wonderful Life"-era Sparklehorse. And in "Blood Bank", the title track of the eponymous EP released in January, there's something elemental – wild, even – in his impassioned strumming, hunched over his electric guitar, that removes it from any comparisons to early Coldplay. It's one of the many moments he sets spines tingling.

If he breaks hearts in "Skinny Love", his falsetto vocal over his skipping guitar, he breaks hearts again in "Flume", his voice telling of the ache of loneliness, but also in "For Emma", and in "Re: Stacks", which he plays solo, seated with just his acoustic guitar for accompaniment. As proof of the reverence that is paid to Bon Iver, a whoop is extraordinarily shushed by another devoted fan.

When he's not playing a wild, frenetic guitar part, Vernon speaks with the coolness of a young rock star, albeit an overly humble one. "It's been an unbelievable couple of years for us. We first played a place here called the Social to about 75 people and there were only supposed to be 40. Now everybody is here to see our show – this tent is filled up – and I can't tell you how much it means, so thank you."

If the album and EP seemed hard to recreate live, Vernon does a stellar job of making it intimate for tonight's crowd. It helps that the atmosphere is trapped into the tent, and he doesn't have a hard task convincing the crowd to sing along to the refrain in "The Wolves" – "What might have been lost" – and making the most of the tent's natural amplification. An encore of country-rock band Jayhawks' "Tampa to Tulsa" is intimate, the four band members forming a cluster in the centre of the stage, Vernon's distinct vocals riding over his bassist's.

If there's a minor quibble, it's that the percussion, presumably to help the show's live momentum, occasionally drowns out Vernon's guitar, especially the melody of final song "Creature Fear". But this song's psychedelic crescendo-ing ending, rather than alienating the crowd, just leaves us even more in awe.