Joanna Newsom, Somerset House, London

In 2007, Joanna Newsom toured her spellbinding, wordy second album Ys backed by international orchestras. Now that Ys has just about sunk in – and acquired a cult classic status – the Californian harpist and singer is back on her own again. On the Somerset House stage, it's just Newsom, her golden harp and her long, golden hair. And those harp-plucking hands, which look like yours or mine, but are anything but. When she hits a bum note – which isn't very often – it's reassuring rather than disappointing, as it proves that Newsom is, in fact, human.

Wearing a floor-length, strapless dress, Newsom makes a nervy start to her set with old favourite "Bridges and Balloons". Her first comment to the audience – "Wow, a lot of white people" – is unnecessary and, from where I'm standing, completely untrue. Blame it on nerves or tiredness: Newsom has just hot-footed it from the Latitude festival in Suffolk, and has had little time to prepare herself for her second performance of the day.

As she starts to play "Emily", however, the spell starts to take hold. The song in question is one of only two tracks from Ys that she airs tonight (the other is "Cosmia"); perhaps the album's grand, Van Dyke Parks-orchestrated setting is more suited to the LSO than one woman with a harp. But "Emily" – a song about Newsom's astrophysicist sister – is pulled off with aplomb. And that voice. When Newsom released her debut album in 2004, her squeaky 10-year-old's timbre had many dismissing her as a whimsical fly-by-night. At the grand old age of 26, Newsom has shrugged off her earlier pretensions and her bright, husky voice soars over Somerset House.

It's a mark of her confidence that Newsom plays a set half made up of new songs – usually, the kiss of death for any crowd-pleasing artist – but the crowd lap them up. The Middle Eastern-tinged "Colleen" has already been a live favourite for a while, but many of the tunes she plays are unrecorded and even, in one case, half-finished. One stands out in particular: a syncopated, jazz-inflected ballad about California that calls to mind Joni Mitchell circa Court and Spark.

As the sun sets and the clock strikes 10, Newsom is back on her harp, finishing her set with "Clam, Crab, Cockle, Cowrie". She shivers and thanks us for coming to see her in a "cold courtyard". The crowd titter at her modesty – we'd have happily watched her in a Siberian blizzard. In the meantime, we await news of her third album with baited breath.