From BASC code of practice for shooting birds
All birds are protected, and although there are seasons when you can legally shoot game, and some wildfowl, they are not suitable quarry for air rifles. However, as long as you are complying with firearms law, you can shoot certain pest bird species. These are covered by general licences which, in simple terms, mean you can shoot the birds listed, provided you have the landowner’s permission and provided you are doing it for one of the reasons allowed by the licence.
These reasons include:
to protect crops
to protect game and wildlife