Sorry, but it makes me want to bang my head against a wall (and I know it's been corrected): hunting is not illegal. Nor is hunting with hounds.
I grew up in the thick of hunt countryside, in a house with farms on two sides, and I have seen a lot of hunting. I have also killed plenty of animals and I don't have the least objection to it. I can't stand the local hunt because they are unmitigated dickheads who do things like riding through my mum's garden, riding into our primary school playground, riding through fields of pregnant sheep and newborn lambs, etc. etc.
I don't particularly buy the idea that a hunt is a quick or humane way to dispatch a fox. I've seen foxes that got away and I've had to put the bodies in the bin after they die in the ditch. I've also seen foxes shot or poisoned that died in pain. IMO shooting is the best, but obviously not if you're a rubbish shot, which matters.
What bothers me about the hunt isn't therefore so much that I think it is wildly more inhumane than other methods of killing an animal that is preying on livestock. My issue is that killing that animal is made into sport for people. That's disgusting. IME, the people who do it tend to be entitled, cruel, unreflecting tossers - and I do think that's a natural result of making sport of an animal dying in pain.