Sigur Ros, Cecil Sharp House, London

With the crowd hushed and the band ready, Sigur Rós front-man Jon "Jonsi" Birgisson purred his diffident, Icelandic welcome. "Hello. Thanks for coming. We're just going to play a few songs before the film." The four-piece began, aptly enough, with "Agaetis Byrjun" – meaning "an all right start".

The band were in town as part of the BBC Electric Proms, for the UK premiere of Heima ("At home"). The film is Sigur Rós's account of their summer 2006 return to Iceland, in which they gave unannounced free performances in a number of locations, from sprawling valleys to village halls. Often it was more fitting, even necessary, to play acoustically. And it was this Sigur Rós that the audience got to see, minus the trademark, swirling soundscape produced by cello bow on electric guitar.

The pared-down songs gave a wonderful glimpse into Sigur Rós's gentler side. The "all right start" was an example of pure musical fidelity, Birgisson's precise guitar and unwavering falsetto nailed to perfection.

The new song, "Heima", came next, showcasing the gibberish "Vonlenska" ("Hopelandic") language Birgisson uses, often to mesmerising effect. And then, "The Nothing Song". Here, the band really got going, the drummer Orri Dyrason creating a lilting rhythm, the bright piano of keyboardist Kjartan Sveinsson driving the melody.

In the plodding "Heysatan", the merry-go-round began: Birgisson moving to harmonium, Dyrason on glockenspiel and Sveinsson playing guitar. If their versatility was impressive, the band's comfort in the song's frequent silences was a thing of wonder. Their heads bounced to an imaginary beat – and the audience moved with them. The song fizzled out, the harmonium giving in with a puff and a wheeze. It all looked so awkward, yet Sigur Rós were at home, lost in their music.

Then Amiina, an experimental string quartet, came on stage. "These are our friends. They help us play. Thanks," said the laconic Birgisson. Two songs – "Samskeyti" and "Vaka" – from the "Untitled" album followed. But it is when the first strains of "Von" struck up, with the almost painful beauty of Amiina's strings, that the audience fully felt a sense of belonging.