The four boys, who met at Leeds University in 2007, looked stunned as they collected the award – despite being the favourites.
The band beat acts such as rapper Plan B and Django Django to win the £20,000 award at the Roundhouse in Camden, north London.
Singer-songwriter Richard Hawley, nominated for his album Standing At The Sky's Edge, narrowly missed out again – six years after controversially claiming he was "robbed".
The result brought disappointment for psychedelic four-piece band Django Django. The band members – David Maclean, Vincent Neff, Jimmy Dixon and Tommy Grace – became friends at Edinburgh School of Art before meeting up again in London and forming the band.
Their self-titled debut album was nominated after reaching No 33 on its debut in the UK album charts.
Other nominations included Plan B's Ill Manors; electro-soul singer Jessie Ware's album Devotion; Brighton-based band The Maccabees for Given to the Wild; and Field Music, set up by Sunderland-born David and Pete Brewis, for Plumb.