"justify the killing of wild animals for fun" I'd include that as trophy hunting, I think.

However, it's my opinion (and observation) that the joy many hunters experience is rather more complex than 'fun'. I am speaking from a Canadian experience, of course. The UK is a vast foriegn culture, and I don't know what constitutes hunting there, other than what one reads about fox-hunting (which is done here with no involvement of foxes, just a smelly bait dragged over the course).

The hunters I know are shocked and disgusted by such things as 'canned hunts', which are no mre than plain abattoir style slaughter, involving no skill and no real confrontation with prey animals.