Hey Alex,
Not sure where you are located in the country, but Woburn (of the Abbey and Safari park fame) was (is?) the largest deer park in the country and keeps ten different species. They also have a lot of land open to the public so there would be a chance of picking one up if you were to pay a visit at the right time of year. That said, I very much suspect that anything found on the land belonging to the estate legally belongs to the estate itself so you would want to get permission if you planned on removing anything. As Max has said, it would be unlikely that they would simply let people wander in and take stuff away.
I guess that you haven't started your flint knapping yet then?
J.