Reading this thread, all I can say is that the UK seems to have some strange notions about property rights. Maybe that is because you have less public land(?). Maybe because the Monarchy used to own all of it(?). Regardless, strange.
As to an easy solution for the 1,000's of dog walkers and other idiots tearing up the forests and woods...introduce some actual predators. Wolves, bears, mountain lions/cougars, etc.
People tend to respect what they fear. Especially when they're not at the top of the food chain.
After a few get mauled, they'll be a bit more observant and respectful. If they die, then Darwinism wins in the end. You're just weeding out the dumb ones. Problem solved.