I've seen a fox killed by hounds. The lead hound chased it over a wall and took it by its throat. The second hound went in to help, and by the time the rest of the pack reached it a couple of seconds later, believe me, it would have been dead. It had run for no more than about a mile.
There are alternatives:
1) Gassing/poisoning. Long, slow, agonising.
2) Shooting. OK if the marksman scores a direct hit and kills outright. If not, the animal crawls away and dies slowly and in pain.
3) It gets hit by a car. Actually, more foxes died like this than were ever killed by hunts.
4) Trapping. Yeah.
5) Flush it out of its den and club it to death, or grab it by the scruff of its neck and shoot it through the head.
6) Just leave it. Foxes DO raid poultry houses and occasionally take new born lambs. This hasn't been too great a problem in the past, but if numbers were to increase, then it would be. Then we'd revert to pre-foxhunting days where an assorted mob would be despatched to kill the animal in whatever way they fancied (see above).
But the debate is somewhat academic now, so we'll just have to wait and see what happens.