MGMT, ICA, London

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Klaxons are in the lobby, Queens of Noize are waiting patiently in the front row; oh look, there's Mark Ronson in the bar, hanging out with Kaiser Chiefs. And, um, Kimberley Stewart (but let's forget about her). If anyone here isn't on the guest list, I'd like to personally congratulate them on being able to get in, because to call MGMT at the ICA a hot ticket would be the understatement of the year.

It's been a long time since a band as uncompromising and (more importantly) fun as MGMT came along. And, like buses, they all came at once, with fellow Brooklynites and world-music enthusiasts Yeasayer by their side.

Tonight, they proved they were worth the hype. Their debut album, Oracular Spectacular, is about to sweep the nation with its poppy, melodic take on prog rock, but live, the band are infinitely more prog than pop. Pocket-sized core members Andrew VanWyngarden (vocals, guitar, dreamboat) and Ben Goldwasser (keyboards, curly hair) are backed by a trio of excellent musicians, and they revel in it, launching into extended psychedelic jams every five minutes or so. Anathema for your average Adele fan, heaven for everyone else. VanWyngarden and Goldwasser have obviously been paying attention in class: the two met while studying music at Wesleyan University in Connecticut, and their music brims with the spectres of David Bowie, the Flaming Lips and Mercury Rev.

By the second song – the psychedelic dream-rock of "The Handshake" – the crowd has already been won. "They can do whatever they want now – they've crossed that bridge," enthuses someone standing next to me. The whole album comes to life on stage: from the melancholy cosmic rock of "Pieces of What" to the Britpop-tinged "Weekend Wars".

The great thing about MGMT, however, is that rare ability to be both experimental and accessible. They can prog out for 10 minutes straight without losing the attention of a fickle industry audience, but it's their pop songs that really win the crowd over. The slo-mo, funked-up "Electric Feel" is a standout, but "Time to Pretend" – their tongue-in-cheek anthem about being a rockstar, having babies with models and yearning for your childhood innocence – is the real future classic. It's obvious that everyone in the venue has already been listening to the song on repeat: they all know the words.

There was not one, but two encores. During the last, VanWyngarden and Goldwasser took to the stage in silly sunglasses to sing the disco-inflected "Kids" to a backing track, while their drummer dropped his sticks to play a hair-metal guitar solo. The fun is back in music; long may it thrive.