Sir Stirling Moss was an early adopter, and was often shown in photos playing with his cars - he also endorsed several sets, including Aurora in the USA. There are clips on the BBC archives.
Jim Hall of Chaparral fame was a racer (and also endorsed the Cox Chaparrals, for a commission), and a few other racers were active as well, even quite recently.
Does this have to be solely UK oriented? I've actually got a whole dossier on "celebrity slot racers", although more US oriented, and a lot of times it was just a one-shot publicity deal (like Robert Kennedy opening a playground in NY that had a slot car setup, and holding the controller the wrong way...).