KAE1,
Its a confusing term. YOU don't need one. In effect, a licence is granted to "any authorised person" to shoot the species I mentioned each year for the reasons of disease control, crop protection etc. Theres a smaller list that cn be shot to protect songbirds etc. Thats the short answer.
The long answer is the killing of wild birds is banned under the Wildlife and Countryside act 1981. It is still legal to kill game birds and poultry but only in an approved manner and only in the right season.
Game birds are pheasant, ptarmigan, partridge, grouse, moor game, black or heath game.
Poultry are domestic fowl, geese, ducks, guinea fowl, pigeons, quail and turkey.
There are other exemptions. Most notably Section 2 which permits certain birds to be shot at any time and others in season by "authorised persons" for legitimate reasons. This exemption is granted annually by Defra (and known as licenses which is confusing).
You are fine with pigeons and corvids provided you have permission and are shooting them for a legitimate reason - see here
http://www.defra.gov.uk/wildlife-countryside/vertebrates/gen-licence.htm
Red