It's not just a British thing either, many Americans do that as well. I think it's gross unless you switch into different shoes (that aren't used outside).

My college roommate walked around with his shoes on all the time, and all the mud and slush (especially in the winters) would get out of control. He stopped doing it eventually after I casually (i.e., passive-aggressively) brought up the conversation. He was from southern California so he had no idea what snow was and how disgusting it makes everything

On the other hand, carpet is better than wood or tile during the winter... it's a much better insulator for heat so you don't feel like you're walking around on ice all the time. You just have to keep it neat.