There may well be too many foxes and I agree that the foxes should not be fed. I think that a cull is not required though, just measures like keeping your waste away from them as already mentioned.
However, there is a much bigger problem IMO and am prompted to reply by the reference to the cat flap. There are too many cats.
This is the elephant in the room when considering nuisance animals. I know this may upset some cat owners but please do consider keeping your pet indoors. They can be just as smelly and invidious as any fox. Furthermore cats, or rather their owners, are responsible for killing thousands of small wild animals including birds.
I am not trying to flame here. I should mention that I am not anti-cat. I am pro responsible pet ownership. This is an issue that, along with dog fouling, we should grapple.