Thanks all… i have fully investigated the shooting idea. Apparently a well-known (to some) BBC commentator supports an unlimited GB crow population leading to a ban (in effect) on the obvious solution. Jeez.
You can shoot them under certain circumstances under General Licence
These are the pest birds you can shoot in England from 1 January 2022 under the main general licences:
Canada goose (GL28, GL40, GL41, GL42)
Carrion crow (GL26, GL40, GL41, GL42)
Woodpigeon (GL31, GL42)
Jackdaw (GL42)
Jay (GL40)
Magpie (GL40, GL42)
Rook (GL42)
Egyptian goose (GL40, GL42)
Monk parakeet (GL40, GL40, GL42)
Ring-necked parakeet (GL40, GL42)
Ruddy duck (GL21)
Sacred ibis (GL40)
Indian house-crow (GL40, GL42)
Feral pigeon (GL41, GL42)
GL21 = kill or take ruddy ducks for conservation purposes
GL26 = kill or take carrion crows to prevent serious damage to livestock
GL28 = kill or take Canada geese to preserve public health and safety
GL31 = kill or take woodpigeons to prevent serious damage to crops
GL40 = kill or take wild birds to conserve wild birds and to conserve flora and fauna
GL41 = kill or take wild birds to preserve public health or public safety
GL42 = kill or take wild birds to prevent serious damage to livestock, foodstuffs for livestock, crops, vegetables, fruit, growing timber, fisheries or inland waters
