As far as I can tell the only real opponents to this are the NFU, who are basically just a mafia of rich landowners cosplaying as a farmers union in order to suppress wages for real farm workers and protect the inequality of land distribution.
If you asked a real farmer whether he would be up for getting compensated - even at market value - if one of his sheep was eaten by a lynx he would say "yes, it would save me the bother of rounding up the sheep and taking it to market therefore making it more profitable. Plus I already lose sheep to people's pet dogs. What is the difference?"
Anyway, sheep farming is the least economically viable form of agriculture in the known universe. As an industry it is basically just an expensive national hobby.