The CIFAS text is rather ambiguous, but I just rang them and they said that their credit checks only apply to individual names, not addresses.

CIFAS reckon there isn't much anyone can do to stop their address being used like this, but it doesn't matter because you aren't responsible for the debt and it won't affect your credit rating.

Think I will register anyway, and stay ahead of the next identity thief - I'm feeling rather pessimistic about it all, and don't always remember to shred my letters. Not to mention the trick with the blutacked stick through the letter box!