The 'U Got The Power' group toured with the 'Pompeii' hitmakers and lead singer Sam Hammond wants to follow in their footsteps and achieve a Number One album.
He told BANG Showbiz: ''We'd love to match what they've done. It's been great for us, when we went on tour with them they were just starting to blow up but reasonably small and it's amazing how quickly they've grown.
''Bastille just really connected with people, their music really connected and that's great. The best way to play it''
Swiss Lips had a great time when they were on tour with the electro-pop group, and got up to plenty of partying.
Sam added: ''There was a lot of drinking and the guys from Bastille like to party. We did our own event at The Union [venue in London] and they came down and played that and hung out.
''That was a big party, but we were well behaved.''
'U Got The Power' is release on April 29.