The Essex group, aged between 18 and 20, are made up of lead vocalist Te Eugene, guitarist Eddie Brett and ukulele player Sonn Murharrem.
Their song 'Lovesick' features the rhyming words "eyes" and "pork pies", reminding panellists Simon Cowell and David Walliams of '80s ska band Madness.
Meanwhile, Alesha Dixon says: "I liked you from the moment you stepped onto the stage because your personalities are shining in abundance.
"You look like you're having fun... I think you're my favourite act so far."
Walliams added: "It's like a great London band. If you brought out an album tomorrow I would buy it."
Britain's Got Talent airs Saturdays at 8.30pm on ITV1.
> 'Britain's Got Talent' auditions week five preview - Pictures
> Stephen Mulhern's 'Got Talent' blog week five
Watch a teaser video preview of The Loveable Rogues' performance below: