Ólöf Arnalds has been knocking around the Icelandic music scene for close to a decade, collaborating with Reykjavik scenesters such as Sigur Rós and working as a touring member of Múm. However, her recent second album, Innundir Skinni (Under the Skin), seems likely to bring her to the fore in her own right.

This intimate London jazz venue was perfect for Arnalds's gentle, fractured freak-folk, a music that sounds alien and rootsy at the same time. The 30-year-old singer-songwriter's trick is to weave hypnotic spells with very little, alone on stage and strumming an acoustic guitar or a charango (a 10-stringed, lute-like South American instrument) to accompany her husky, spectral vocal.

Her exotic, quizzical songs were rendered even more alluring by being largely performed in Icelandic, though she switched to English for the halting, Joanna Newsom-like dream-pop of Crazy Car. Between songs, she was a maverick and charismatic presence, given to charming non-sequiturs and veering into seemingly inconsequential anecdotes with the self-mockery and timing of a natural comedian.

Arnalds's choice of covers was similarly idiosyncratic and adroit. Her croon through Hank Williams's Please Don't Let Me Love You was affecting without suggesting that Icelandic country and western is a genre ripe for development; her take on Gene Clark's With Tomorrow was suitably lovelorn. Best of all was a strum through Bruce Springsteen's I'm on Fire that transformed the original's carnal urgency into a delicate reverie.

Of her own material, the standout track was Surrender, which features keening counter-melodies from Björk on the album, but sounded wondrous even without that singer's crystalline embellishment. Arnalds is unlikely to be playing venues this intimate for too much longer.