Crows, magpies, Jays, rooks etc are still on the general licence (which defra issue every year) so can be legally culled but only if dining on a field of cereal crop etc.
The plastic hawk idea wouldn't ever work. I've personally watched crows bully Buzzards which are 4x bigger than them. Crows simply, have no fear. The only thing they are fearful of is a human & gun. They might not know what a gun is but they know it means danger.
Technically, i could lawfully shoot them with a rifle (i have many different calibres) if one landed in my garden, because i have an open firearms licence. Provided, the projectile (bullet) does not leave my boundary i have committed no offence. But it would be madness to use a rifle in suburbia because of the risk of ricochets. A shotgun would safer but are incredibly noisy. Plod would be round here in minutes.
I literally have no idea how to stop this.