Wildcat extinction is an extremely specific issue. Wildcats only exist in Scotland now, driven to near extinction mostly by humans, not mating with other cats. This happened literally hundreds of years ago and has practically nothing to do with house cats. Now interbreeding is an issue for the preservation of the small number of wildcats left in Scotland. It's sad but hardly a concern for keeping cats in most areas of the UK.
Secondly, I do ignore that cats are 'bringing in foxes and badgers'. Can you present a source on this? I couldn't find anything.