The south London band won the $30,000 prize over 11 other shortlisted acts at a ceremony in London Tuesday.
The group beat its more well-known competitors, which included bookies' favorite Paul Weller, singer Corinne Bailey Rae and past winner Dizzee Rascal.
Frontman Oliver Sim said he was stunned by the news: "I don't know what we were expecting but we weren't expecting this."
The award has honored the best album of the year by a British or Irish band since 1992. Previous winners include the Arctic Monkeys and Scottish rockers Franz Ferdinand.