I have to agree with this bit of your comments, Alan, up to a point.
Predators cannot increase beyond the extent that there are enough
prey species to support them, fair enough.

But there is nothing to prevent them from increasing the range of
species that they prey upon. The bigger the range, the more foxes
it can support.

Man has introduced several things that foxes now include in their diet,
(rabbits, domestic cats, pheasants, chickens) that were not originally
available to them, so we are to blame there.

At the same time we have destroyed any natural predator they may
have had, another lack of foresight on our part.

We are very good at meddling with things we don't understand, like
the natural order of things, then we cry like spoiled kids when our plans
go pear shaped.

Shooting is not a viable long term solution, better to find some way to
redress the natural balance, but in order to do this we will need a far
better understanding of what we are dealing with. This will require
those on both sides of the argument to put aside their predisposition
for rhetoric and dogma.