Taken from the government website...
https://www.gov.uk/control-dog-public/overview
Part 1:
Overview
It’s against the law to let a dog be dangerously out of control:
in a public place
in a private place where the dog isn’t allowed to be (eg a neighbour’s house or garden without permission)
The law applies to all dogs.
Some types of dogs are banned.
Out of control
Your dog is considered dangerously out of control if it:
injures someone
makes someone worried that it might injure them
A court could also decide that your dog is dangerously out of control if:
it injures someone’s animal
the owner of the animal thinks they could be injured if they tried to stop your dog attacking their animal
A farmer is allowed to kill your dog if it’s worrying their livestock.
Penalties
You can be fined up to £5,000 and/or sent to prison for up to 6 months if your dog is out of control. You may also not be allowed to own a dog in the future.
If you let your dog injure someone, you can be sent to prison for up to 2 years and/or fined.
If you deliberately use your dog to injure someone you could be charged with ‘malicious wounding’. The maximum penalty is 5 years in prison
So I'm afraid your neighbours don't have a leg to stand on, they broke the law and are liable. The police should be involved, the next time it could be another animal, child or adult.
Edit: I read this as being common law and not a tort, maybe I'm wrong tho.