..and FFS do not use an air rifle on a fox even if it is a .25 FAC gun and even then it would be touch and go. Legal limit air rifles are ok on rabbits and most things down in size from that and even then you need to be a good shot (half inch groups at 35 yards maybe). Shotgun or pest controller and that's it really.
Another thing about foxes in chicken coops – so they kill all the chickens and yes this is bad news all round (not for Foxy though). Doesn't sound dissimilar to dogs running wild in flocks of sheep or indeed, dogs let loose in a chicken coop. I don't hear many people calling for dogs to be snared, clubbed or shot!
In the countryside Foxes cause a problem with poultry and or game birds but they also do a lot of good preying on rabbits so it is 6 of one and half a dozen of the other really.
Many shooters would do it for free but definitely not in an urban context you'd get an ARU round in no time.