The band's new cut 'Of The Night' is currently leading the midweek chart, fending off competition from Gary Barlow, Lily Allen and Ellie Goulding.
"It's a bit surreal for us to be anywhere near the top 10, especially with people like Lily Allen and Gary Barlow," frontman Dan Smith told Digital Spy.
"For a track that we made for a bit of fun as part of one of our mix tapes over a year ago to be competing with such big names is completely mental."
He added: "We're massively grateful to everyone who's supported and bought the track and EP."
Bastille's 'Of The Night' is a mash-up cover of Corona's 'The Rhythm Of The Night' and Snap!'s 'Rhythm Is A Dancer', which originally appeared on their Other People's Heartbreak back in 2012.
The new single version will be included on the upcoming repackage of their chart-topping debut album All This Bad Blood, which will be released on November 25.
Watch the music video for Bastille's 'Of The Night' below: