He accepted the £20,000 award at a ceremony at the Roundhouse in Camden Town, north London.
Speaking at the awards, he thanked his parents for teaching him to be "self-sufficient".
He beat 11 other acts, including David Bowie and bookies' favourite Laura Mvula.
Other nominees included previous winners Arctic Monkeys and singer-songwriter Jake Bugg.
The £20,000 prize is open to British and Irish acts and aims to reward the best album of the year.
Earlier, Foals frontman Yannis Philippakis fought off the flu to open the show.
The London band were one of the acts shortlisted.
Philippakis said there was "no pressure" in opening the show.
He said: "It's nice just to get it done so we can enjoy the night."
Bowie, who rarely plays live now, did not perform at the event.
Instead, fans were shown the video for Bowie's track Love Is Lost.
Once a prolific pace-setter, Bowie had withdrawn almost entirely from the public eye in recent years and had released no albums for a decade.
But without warning earlier this year, he suddenly released the single Where Are We Now? and announced his comeback album, which was warmly received by fans and critics, as were the accompanying videos.
There have been persistent rumours of ill-health for the New York-based British star, but these have been repeatedly denied by his representatives.
The list, which included five debuts by the likes of 19-year-old Jake Bugg and Disclosure, was drawn from 220 albums submitted to the judging panel.
Bugg, who was second up on stage, performed Lightning Bolt.
The other first-timers were Mvula, Savages and Rudimental.
Inclusion on the shortlist usually ensures an instant boost in sales for nominated artists.