I am not sure if any 'wild bird' survey or count should include the pheasant, it is not a natural British species after all. They are an Asian species that seems to have been introduced for food all over Europe and the British Isles by the Romans. That means they have been here c2000 years so they are now pretty British I suppose. However, If they were not bred specifically for 'sport' then there would be no pheasants here at all. It is only because they are farmed and habitat is managed for them that they survive.
What I find distressing is the practice of some gamekeepers of killing all possible predators of young pheasants so that people can pay for the 'pleasure' of doing it. How many birds of prey are illegally poisoned because they might have an impact on farmed pheasant numbers?
There seem to be less pheasants in Dorset than where we used to live in Hampshire. On the main road from our village to the nearest town you would see countless dead pheasants killed by cars and yet the local gamekeepers would complain that they lost pheasants to foxes and buzzards! Hypocricy rules it seems!