The soon-to-be-married couple was spotted on a date Tuesday. They got in line for the London Eye ferris wheel -- like everyone else -- and eventually took it all the way to the top. Once they were alone, the Biebs and Hailey locked lips like there's no tomorrow.

After the smooch fest, Justin busted out a guitar and got in his element to serenade Hailey outside Buckingham Palace. She looked doe-eyed and smitten by her guy's romantic gesture.

Justin professed his love for Hailey as he sang in front of the crowd that naturally gathered around them.

It's kinda been their thing lately -- make out in public here, there ... and just about everywhere else.

The international trip takes place on the heels of Bieber and Hailey hitting a courthouse in NYC last week to get a marriage license. A lot of people -- including Hailey's uncle, Alec Baldwin -- think they already got hitched, but we're being told that just isn't so.

They may be heading to the altar soon enough though, especially since they now have their marriage license. Sources told us they'd be tying the knot outside the country ... and they're definitely not in the U.S. of A. right now.