One legal definition of farmed deer (and I say one because basically you keep looking for legal definitions until you find the one that suits you
) is that any enclosed deer kept for the purpose of business are farmed. To my mind that means all park deer are farmed. Do you know any park owners who give away the carcasses to a game dealer, who never spend any money on fencing and food and who would give you a trophy stag rather than accept £10,000 for it? Of course not because they are all running a business.
Sharkey is absolutely correct to raise the issue of huge "parks" that call themselves wild but can supply you with breeding stock through their handling system. Likewise the "farm" that has no handling system and shoots everything in the field. This is basically a "park" system but he can still choose to have a farmed game handling facility licence and supply all year round.
Sharkey obviously thinks along the same lines as me because when one particular meat hygiene inspector decided to make life difficult for me and said I had to choose between park or farm status I said I would have both. "No, you can't do that. It has to be one or the other." So I asked "Is it illegal to own a deer farm" Answer "no." "Is it illegal to own a deer park?" Answer. "no"
"So then how can it be illegal to own both?" That did not make him happy.
Basically deer law is in a mess, always has been, always will be while we have so many wealthy land/park owners in a position where they make sure no legislation is passed that might upset them. With regard to TB and other disease control and other animal welfare issues there can really only be two categories; completely unenclosed or enclosed. Their wildness or tameness doesn't come into it.
If you have enclosed them you have taken away their natural options on how to survive and from that point on you are totally responsible for their feeding and welfare whether you can step up to that challenge or not.
I have seen parks that look after their deer brilliantly and carry out all the procedures you might expect on a "good" farm. I have also seen "farms" that should never be allowed to stay in business. As with everything it all boils down to the individual in charge.
I am sure you will have gathered by now that I am having a little rant! but facts are facts.