Chris Packhams group Wild Justice have legally challenged Natural England and the way they issue the general licenses for pest control and 16 species of birds. Corvids, pigeons etc.
Basically at the minute NE say that the shooter has to decide if all non lethal methods of control have been used and lethal force is the only way forward to control the pest. WJ say that this is irresponsible on NE part and it should be NE that decides if lethal force is necessary not the shooter or controller. NE couldn't defend the challenge so have had to remove the general licenses immediately and instigate a review of the system.
Basically it looks like you will have to apply for a license to shoot pests in the future from NE so that NE have confirmed it as the only course of action available not the shooter making that decision. This could be a slow process and not always be granted.