Foxes are a protected species, so be careful what you do.
I think you're right about them not being protected. However, every effort should be made to deter them by humane methods.Hunting foxes without hounds is still permitted and they don't appear on the list of protected species at naturalengland.org.uk.
GC
OK, but they are not regarded as vermin, so it's not legal to kill them for no reason.
Not only that, they make a truly godawful racket in the night, barking, growling and rampaging around (actually it's quite funny), and they leave their horrible stinky sh1t everywhere. Reviews of deterrent products seem to vary - has anyone found a method that really works? I don't mind them being around, but I don't really want them setting up home in my garden and trashing it.
The usual other options - poisoning, trapping etc. are also a compete no no, so you are left with trying to discourage them. Good luck!