the lass on the phone said that because the general licence does not expressly state what CANNOT be shot, then it is not therefore illegal to shoot pheasant. However she did issue some guidelines for such circumstances and they are as follows:
They must only be shot during the legal season.
They must be humanely dispatched
You must have the permission of the owner of the land (or the owner of the shooting rights for the land) on which you are shooting.
It does not matter who bred the pheasants as by the act of landing on your permission they have transferred ownership to the owner of the land.
It does not matter that they are game and not vermin. Air rifles are not forbidden for game hunting as long as they are not used in a way which causes unnecessary suffering.
Hope this clears things up for those who shoot or are interested in getting into shooting...