I've just had a quick look over this thread, and I've not spotted (though might have missed) the important point about game rights vs vermin-shooting permission.
In order to shoot game as far as I'm aware you need permission not from the landowner or the tenant, but from the holder of the game rights: who might well be neither of those two.
We have always known there were two Britains: one extraordinarily pleasant, inhabited by mild, tolerant, kindly people; the other utterly disgusting, inhabited by brutal and malevolent louts. Auberon Waugh