My daughter had a problem with pigeons living on her house roof - the droppings were a health hazard, especially with her children around - she was told that the only legal way to remove them was by shooting so there's definitely no legal worry. Having said that someone shot a pigeon which 'fell to earth' on our allotment and it was merely injured, so if you're going to shoot them make sure you do it right. I admit they're a pest but that's no reason to cause unnecessary suffering.