Some old farm folk will remember the War Agg Dept who came in and told farmers what was going to happen!I think you underestimate how much control the government has over the way people manage their land, and what they can or cannot do on that land.
With regard to pest control, landowners are already compelled to control rabbits, rats and certain weeds, for example. Whether or not this is properly enforced is another matter, but if it is then landowner has no choice in the matter.
There is already mention of a "deer management element" in the latest round of agri-environment support schemes, so that's just one step short of compulsory reduction in numbers.
With individual fallow herds numbering in the thousands in some areas, it's going to happen.
All the scrub land was ripped up and they had to get it producing food,
That will only be in a different name these day but if needed just as much clout