Under section 161 of the Highways Act1980, it is an offence for any person, without lawful authority or excuse, to discharge any firearm within fifty feet of the centre of any highway which comprises a carriageway, if in consequence, any user of the highway is injured, interrupted or endangered. For these purposes a carriageway means a highway (other than a cycle track) over which the public have a right of way for the passage of vehicles. Air rifles above 12ft/lbs are classified as a Section 1 Firearm and requires a licence (FAC) otherwise known as a firearms certificate, and an Air pistol above 6ftlb is a prohibited weapon.
The following are considered pests.BIRDS: (covered by the open general licences) crows, rooks, jackdaws, magpies, jays, wood pigeon, collared doves, and feral pigeons.
MAMMALS: brown rats, grey squirrels, stoats, mink and rabbits.
If its not possible to be absolutely sure of killing any animal or bird humanely, then it should not be attempted.