Probably because cats have been there for so damn long, it just doesn't matter any more. They've integrated into the natural wildlife. Or did cats originate in the UK? I would have thought they would have been brought over by the Saxons, or perhaps the Romans.
Man doesn't so much create problems, as define them. We could simply let cats go nuts, abolish all quarantine control, and let evolution take it's course, and it wouldn't necessarily be a problem.
But we've decided we want to keep our native wildlife the way it is, for as long as possible, so having imported animals here is a problem. And the only way to fix it, is to separate those introduced species from our native wildlife, as much as possible.