The fact is it is a criminal offence, a recordable crime, to be in charge of a dog in a public place which causes injury or fear of injury. That the dog is young, easily excitable, or votes lib dem is utterly, completely irrelevant. It. Is. Simply. A. Crime.
Period.
If it had simply frightened you it might be appropriate, assuming the owner was suitably contrite, to deal with the matter informally by way of a community resolution. Something like a sincere written apology, or an undertaking to take the dog for training an keep it muzzled un public, that sort of thing. A community resolution requires that you agree to it as an outcome, it cannot be thrust upon you as a fait accompli.
However, you were actually attacked and injured by this animal which ups the ante somewhat. This makes a community resolution an inappropriate outcome, unless you feel sorry for the owner and agree to it.
It should be investigated as the crime it is and, assuming the evidence is there, the owner should be interviewed under caution in a police station. If the injury was minor, if its the first time the dog has done such a thing, and (most importantly) the owner makes a full and frank admission then they may be eligible for a disposal by way of a formal police caution.
If it is not a one off, or if the owner refuses to make an admission then (against assuming the evidence supports it) they should be charged and sent to court.
It really does seem that you are being fobbed off by a Bobby that does not understand the law, procedure, current policy, and likes to throw in a bit of jolly victim blaming for good measure. I do wonder if the copper, willingly or subconsciously, thinks you might be a bit soft or easily bamboozled because of your seniority.