Shooting rooks in someone else’s garden

We have lots of tall trees with a large number of rooks nesting in them in our garden. On three separate occasions over the last two years, people have shot at and killed the rooks. Twice, they entered our garden without permission, and once, they shot at the birds from a neighbouring field. We do not want the rooks to be shot but are unsure of the law regarding the circumstances in which they can be killed. Please advise.