The band's first collection began at number one on today's album chart update (March 6), and is currently 6,500 copies ahead of Stereophonics' latest set.
"I'm sure it won't stick around there for too long, but it's nice to be there for a day or two," singer Dan Smith told Digital Spy. "It's pretty weird.
"It feels like a bit of a joke to be honest. Stereophonics are like a proper band, and last week we had the weird single chart battle with artists like One Direction. It's been quite a surreal couple of weeks."
He added: "The album thing is ridiculous and we don't really know what to think."
Asked if he had an inkling that they would perform well in the chart considering their steady rise, Smith confessed that they've never judged how popular they have become.
"We're quite new to this stuff," he explained. "We're so involved in touring and gigging that it's quite hard to have a perception of how many people actually like our music.
"It's just been a really nice surprise I guess. The amount of people who have bought it within the first few days - we're just completely blown away."
Bastille's debut album Bad Blood is out now and features their recent single 'Pompeii'.
Watch the music video for Bastille's 'Pompeii' below: