We do not have a leash law. If I ever had a dog I would have no real need for a leash anyway, I don't think it's right. You should train your dog so he doesn't go running off everywhere as far as I'm concerned. Every dog I've lived with (friends dogs) didn't need leads.
To be honest it looks like Wollaton Park to me (up the road from my house, incidently where they filmed some of Batman: Dark Knight which is coming out soon) and they have deer roaming round the estate and they're quite tame. Probably because we don't hunt them down and kill them like in the states.