It is not illegal under The Wildlife and Countryside Act to shoot Canada geese with an air rifle or either rimfire/centrefire rifles.
However, you will need to ensure you have the authority to do so listed on your firearms certificate conditions. i.e. for the shooting of Canada geese, pest birds, or any lawful quarry or similar must be stipulated.
If your firearms certificate does not have the necessary condition, then you cannot shoot them with the rifles listed on your certificate.
Rifle shooting of geese is not sporting and should only be used as a control and management method in a safe area with relevant safety zones and backstops in place.
The shooting of Canada geese with an air rifle, although not illegal, is not recommended on welfare issues.
Lead shot restrictions do not apply to rifle or air rifle shooting of wildfowl.