Isn’t there some sort of archaic law whereby if you put an access into a public area from your garden then it becomes a right of way for the general public, i.e. anyone is allowed to access the park through your garden?
I vaguely remember something about this in the news years ago when a load of walkers started going through someones garden and they couldn’t do anything about it. Plus they weren’t allowed to remove the gate as it had become a legal right of way.
Or have I got it completely wrong….???