Here you need permission to shoot/take game on the land you intend to shoot. This doesn't have to be paid for but that is a private matter between the owner of the land and the shooter.
You cannot just go hunting on public land although some public land will have access granted for shooting purposes for population control and to harvest the meat. What you have to realise, here in the UK the public land is relatively much smaller than that in the States and you will often come across walkers or other land users making general hunting quite dangerous and usually not allowed unless the land gets closed to the public.
There are estates across the country that will offer paid stalks with and without a guide, these are expensive and you will most likely need to buy a tweed hunting jacket as well
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Most hunters will try and cultivate an agreement with a local farmer or land owner and then things can be a lot cheaper (and often exclusive) and many will jealously guard their patch and keep their farmer friends close.
There are so many deer here now (according to the British Deer Society - more than there ever has been) and so few hunters taking them that it can be relatively easy to find a hunter who will let you shoot with them or a land owner who welcomes the control.
There is a move to stop meat getting in to the food chain if it has been shot with lead bullets but I'm not sure how far that has gone. But luckily as a farmer I don't need to worry about that just yet and we just shoot for our own consumption. We farm a few thousand acres and between us we take a few dozen deer each year along with pheasants and partridges and one deer can last me a long time, we rarely make much of a dent in the population.