The appearance is part of Virgin Media's SpeedWeek50 experiential event. The seven day programme began on Wednesday and is designed to showcase the company's 50MB broadband service.
Bluewater will be branded with Virgin Media LCD posters, publicity material and a SpeedWeek50 display beamed onto the Bluewater cliff.
As part of the event shoppers can challenge friends to a race on a Formula 1 Scalextric track and play the new Codemasters Colin McRae: DiRT 2 game on Xbox 360. Visitors will also be able to road test Virgin Media's 50Mb broadband.
Other Virgin Media products being demonstrated include the V+HD box, which pauses, records and rewinds live TV, or TV On Demand. The service provides instant access to thousands of TV shows, music videos and films.
Button will take part in a live Q&A session hosted by the BBC's David Croft after the race.
Bray Leino is orchestrating the event in partnership with retail marketing specialist iblinkworld.