No, I would like to think most people who oppose it do so in support of animal welfare. You get similar antipathy for (for example) badger culling, which isn't seen as an upper middle class thing.
End of the day, I think most people, rabid animal rights people aside, would accept that with no apex predators in this country, it falls to man to organise things; it's just the the arguments for fox hunting in the traditional manner no longer count for much. People see farmers making do with three wire fences and think, 'well, it's no wonder you're losing livestock'. If I left my house unlocked, somebody might well steal my computer at some point - but I couldn't justify roaming around and shooting (much less ripping to pieces with dogs) people who look like they might be responsible. Ridiculous extremes example of course, but seriously: there is no way to physically keep foxes away from lambs or chickens?