School of Seven Bells, ICA, London

Alejandra Deheza, lead singer and guitarist with School of Seven Bells, says she's a lucid dreamer, able to control her nocturnal reveries and mould them to her desires. And this show is not unlike taking a trip through a dreamscape of her and her bandmates' imagining. School of Seven Bells comprises guitarist Benjamin Curtis, formerly of Texan space-rockers the Secret Machines, and identical twins Alejandra and Claudia, formerly of ambient post-rock outfit On! Air! Library! Their voices are identical, too, making their vocal harmonies as ethereal and unnervingly siren-like as the instrumental accompaniment.

The band's unusual name is taken from a semi-mythical South American pickpockets' training academy, which was (perhaps, though probably not) active in the mist-encircled Andes outside Bogotá during the 1980s, and which excited Alejandra's magical realist mind when she learned of it while watching a late-night US television documentary. The band's sound, too, is suitably otherworldly: a drum machine leads the way through the swirl of ambient electronic sound that persists even between songs, Curtis's guitar effects, and the vocals that float above them.

Beneath all that noise is a set of really quite exquisite pop songs, as evidenced on the band's superb 2008 debut album, Alpinisms. After leaving their respective former bands (and, in Curtis's case, his brother Brandon, the Secret Machines' bassist and vocalist), the trio moved into a home studio to live, and to record their euphoric, cacophonic melodies and wrap them around Alejandra's enigmatic lyrics.

The band's shoegazer tendencies are even more obvious live than on the record: the churning waves of distorted chords, the delicate, indecipherable vocals and the psychedelic light-show all owe a debt to the influence of My Bloody Valentine and their ilk, with the sound souped-up and smoothed out for Noughties sensibilities. It's alluring, but it does also mean that every song sounds very much like the last.

Yet there are stand-outs: "My Cabal" is a gossamer wash of synths and lunar imagery; "Iamundernodisguise" is a repetitive round of tribal drums and chanting that builds into a pounding electro-chorale; "Half Asleep" is a pop tune that could belong to the Sugababes, were it not for lyrics such as, "What begins as an unguarded train of thoughts slowly can become/ an addiction to the slumber of disconnection... "

Their encore is the epic "Sempiternal/Amaranth", a slow-building rock chug with yet more impenetrable lyrics and the final, long-repeated line (which I had to identify using the CD sleeve): "Allow yourself to be relieved", which conjures unfortunate thoughts of enforced urination. Though the songs themselves are muddied more than they might be in performance, School of Seven Bells put on an engrossing live show, the hazy video projections only serving to submerge the audience ever deeper in their stellar thrall.