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ninalanyon Interesting point. I am not a solicitor so I don't know how it would be regarded legally, but from what I knowledge I have gleaned of the law:
Criminal damage (to the owner's property)? The dog owner had probably not intended to kill anything; whereas "criminal damage" might suggest a wilful act in law. However, she can hardly claim to have not known or thought the dog should be kept on a lead, and she seems to have made no attempt to control the canine, to obtain veterinary care for the bird (via the staff), offer to recompense the owner or even show any remorse or apology.
"Working animals"? I don't think there is any such distinction in British law,
but....
... Causing unnecessary suffering to an animal? I think that is the proper name of the charge, from reading reports of cases under it. By this charge it does not matter if the animal is a pet, a "working" one, farm livestock or wild. She might argue she had put the injured bird out of its misery - but from the evidence we have, her negligence allowed her dog to injure it, and she had made no attempt to determine if it could have been treated.
Civil action? That would still need sufficient proof of the woman's identity and link to the act, and that's where the difficulties start.
I don't know if anyone managed to obtain the car number. The newspaper report does not state that happening, but it's possible nobody was close enough to see it, or witnesses were too shocked and angered to think about noting it.
If a dog owner allows the pet to attack farm animals, the farmer is allowed to shoot it. Dog attacks on livestock are a serious and very distressing problem, and in one case a cow was killed by a dog or dogs driving it over a cliff. Such shooting is of course neither possible, nor desirable, in the case of dogs attacking pet animals in a garden open to the public, even if the owner or any staff member is a licensed gun user and has a suitable weapon to hand.
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Though a totally separate matter, a vet writing in the same paper that reported the above, expressed her horror at someone publishing on-line a video of trying to give a cat a bath. The images were apparently made for "entertainment" or "fun", showing the brute wearing heavy gauntlets as protection from the terrified animal's inevitable struggling and fighting by teeth and claws.