The idea
The hunted fox has a chance to escape. With the law as it is a bullet is the end. Foxes are vermin. Vermin like foxes have to be eradicated as they take animals higher up the food chain (lambs, piglets, chickens etc) which farmers are trying to produce for our consumption. If we hunted rats would people care? As recently demonstrated in Hackney with the attack on the twin girls by a fox, they are NOT like fluffy pet dogs but vicious predators who's numbers need to be controlled. Hunting with dogs is a tried, tested and succesful method of control.
Why is it important?
I believe in the livelyhood of the people involved from feed merchants to farriers to directly employed hunting staff to name but a few who would be unemployed otherwise.