Accepting their award the band said they couldn't believe they had taken the prize with acts like Noel Gallagher sitting in the audience.
An emotional Ellie Rowsell - the band's lead singer - was brought to tears as she thanked the judges for the prestigious music award.
The four-piece London band - who met as teenagers - then performed live, joking that they "needed a Jaegerbomb" for Dutch courage before heading back to the stage.
Indeed, they joked with Sky News ahead of the announcement that they would: "Down 15 beers before sit down. Ten more after. Get up and play and then ruin it. And then go home and cry."
Luckily, the only tears spilled at the event were happy tears of victory.
Their album - which is their second studio record and second nomination for the prize - is a mix of pop, grunge and indie rock guitar.
Ahead of the ceremony, the band told Sky News they thought they were "too pop for rock, and too rock for pop".
They described their performance on the night - which Rowsell performed barefoot - as having "end of school prom vibes".
The band - who are off to Australia on tour tomorrow - had joked the first thing they would do was "call their mum".
They said while winning the award "would be a nice accolade", it would not change what they do as performers.
Speaking to Sky News during rehearsals, they said rock hasn't been a fashionable genre of late, with band member Joel Amey admitting a guitar group hadn't really stormed the charts since he was a teenager.
The ceremony itself - which featured performances from each of the 12 nominated acts - was opened by Florence + The Machine, with the emotional and raw song Hunger.
Noel Gallagher - who was nominated for the first time as a solo act Noel Gallagher's High Flying Birds - and rock band Arctic Monkeys both represented their work with pre-recorded videos.
While Arctic Monkeys - who have won the prize once before - had the excuse of performing in Sheffield and so missing the show, Gallagher was in the room, watching along with the rest of the audience.
Despite the strangeness of watching filmed footage of Gallagher's band performing Holy Mountain during a Jools Holland show, the song was met with a positive reception.
The first standing ovation of the night went to jazz band Sons Of Kemet, who sang an energy infused track from their album Your Queen Is A Reptile.
The winner was chosen by a panel of independent judges, including singer-songwriters Marcus Mumford, Ella Eyre and Jamie Cullum.
The prestigious award aims to recognise artistic achievement across the whole spectrum of music genres - deciding on just one winner to take home the trophy for album of the year.
This year, rock, pop, R&B, jazz, and grime were all represented in the eclectic mix of shortlisted acts.
However, while the award celebrates musicians at all stages of their careers, just three of the album's in this year's final 12 were debut works.
Novelist with Novelist Guy, Jorja Smith with Lost & Found and Everything Is Recorded with a record of the same name were the newbies in the pack.
Traditionally, the winner of the award also receives a massive boost to their audience following the exposure the music accolade naturally affords.
© Sky News 2018