The “genre-hopping” electronic quartet, who met at Leeds University in 2007, were favourites last night with their debut album An Awesome Wave.
They were presented with their trophy at the Roundhouse in Camden, north London.
Singer songwriter and former Pulp member Hawley, at 45 the oldest artist to have made the shortlist, was previously nominated in 2006 for Coles Corner and had been a hot contender, although he lost out to Arctic Monkeys.
When Monkeys frontman Alex Turner collected the prize, formally known as The Barclaycard Mercury Music Prize, for his album Whatever People Say I Am, That’s What I’m Not, he announced: “Someone call 999 – Richard Hawley’s been robbed.”
The prize gives a huge boost to sales for the victor as well as valuable publicity to all nominees.
Simon Frith, chair of the judging panel, said the shortlist “showcases a wonderful variety of musical voices, emotions and ambitions”.
He added: “There are eight debut albums on the list and four albums from more established artists.
“The sheer range of music here celebrates the abiding ability of British musicians to find new ways to explore traditional themes of love and loss while making an exhilarating soundtrack for life in 2012.”
Last year saw the first time a previous winner has taken the prize for a second time, when PJ Harvey picked up the award for her Let England Shake release, while other past winners have included Dizzee Rascal, Pulp and Klaxons.
Also on the 2012 shortlist were rank outsiders and Leeds-based jazz outfit Roller Trio; Field Music; Django Django; rapper Plan B; Jessie Ware; Maccabees; Lianne La Havas; Michael Kiwanuka; Ben Howard and Sam Lee.
Commentary was from Leeds’s own Corinne Bailey Rae.