Yes, that's the way around here. By German law, animals are things with special protections against cruelty. Much like, e.g. a car, the animal therefore can't be the guilty party. It is the responsibility of the "driver" to control the thing so that it does not cause harm.

You loose control over your car and somebody dies? The controller is charged with involuntary manslaughter. You loose control over your dog (e.g. dog runs across street, lorry has to evade, lorry kills pedestrian) and somebody dies? The controller is charged with involuntary manslaughter.

I would actually be surprised if the UK treats this differently.