There is no barrier to who can hunt, apart from living close enough to the right kind of area and being accepted by a given hunt group I guess, it is not 'restricted' to nobility/royals etc. It costs more than it would In the USA, horses, hounds, tack, social commitments and so on is going to add up to more than the cost of a gun and a permit for you over there I'd guess. But as firearms are so controlled over here (not necessarily a bad thing) fox hunting could, and I say could, be seen in the same light as how the US sees say duck hunting, only fox hunting isn't protected by a constitution, just unwritten laws, tradition and unwritten constitution, which in the face of modern political correctness have no chance...but then again nanny Blair likes the old fashioned First Past the Post electoral system that gives his party an approx 3% advantage over the Conservatives, ahem.
I personally am very worried by any law the is a 'You can't' law outside of criminal activity.
I am not sure who in current mainsteam UK politics you think would be 'Socialist', becuase Labour hasn't been that for a while now.
As for actions in protest against the ban, one nice thing that has been done is a few farmers near Salisbury plane have had till now a 'gentleman's' agreement to let the militray use their land, they have now told the army that is no longer the case because of the ban. Nice, legal and news worthy in a non sensationalist way.