Just to clarify - people "have a right" to shoot things in this country, provided they have the appropriate gun licence, and the landowner's permission. In the case initially discussed on this board, I think the person wasn't in what you'd call a "public place" - it was his garden, I believe. In fact, not many areas are actually "public places" - though you might be forgiven for thinking that, given that people feel free to roam through the countryside at will.
For example, although there is a public footpath which crosses the field at the back of my house, I do get a bit cross when/if people come along to take rabbits etc without asking my permission first. Wildlife knows no boundaries and wild creatures are what you might call "opportunists" and will frequent places where food is easily and readily accessible, hence the huge increase in the numbers or "urban" foxes. The same applies to squirrels - and rats, come to that - so don't be surprised if you see them in your garden! All welcome to come after the rabbits here - but please ask me first!