Yes, it is possible that they could
How close were others to your dog at the time of this?
OK. So nobody was close to your dog at the time of this?
Have there been other incidents with your dog?
It is quite unlikely they would prosecute.
They can't use the Dangerous Dogs Act 1991 because this is not aggression towards a person and nobody was close the incident so there could be no reasonable apprehension of injury.
They could drop down upon the Dogs Act 1871 which does include attacks upon other animals although there is caselaw that says that one incident is not enough unless it is exceptional. The problem with words like 'exceptional' is that it is always possible for a court to find a way of bringing the facts within it though. That is a civil matter though anyway.
On a first incident they would normally just suggest an ABC contract with a requirement of muzzling though.
Can I clarify anything for you?