LazyJane, you have completely utterly misunderstood the DDA (1991)
Section 3.1 refers to "dangerous dogs" in public places, I think this is the section you keep bleating on about. It reads:
^If a dog is dangerously out of control in a public place?
(a) the owner; and
(b) if different, the person for the time being in charge of the dog, is guilty of an offence, or, if the dog while so out of control injures any person, an aggravated offence, under this subsection^ (House of Commons Library, 2013 )
So to try and explain it more clearly, prosecution can only occur if the dog is dangerously out of control at the time the injury occurred A dog on a lead, by default, is not dangerously out of control, but lets assume that you don't believe this to be the case, which I am sure you won't, I will pretend that dogs on leads are not automatically assumed to be under control and try and explain the law for you in a way you should understand.
A dog, on a lead, walking to heel, by his owner's side, is the very definition of a controlled dog. If a child should happen across that dog and decide to run up and whack it on the head with a stick and the dog reacts like a dog and snaps at the child causing minor injury, it will not be assumed that dog (still on a lead, still by his owner's side) was dangerously out of control. There is not a single canine behavior expert in the whole entire world, who would state that the dog in that instance was out of control. The reason for this being that if the child had not approached the dog without permission and had not caused it pain, the dog would not have reacted. The child and the parent who allowed the child to act that way, were the ones who instigated the incident, therefore it was the child and parent who were out of control, not the dog.
In other words, it is your responsibility to control your child. It is not up to the dog owner to prevent your child causing their dog pain or fear, it is up to you.
It's also worth bearing in mind that in the eyes of the law, dogs are property, much like mobile phones. If your child runs up to me and snatches my phone out of my hand and proceeds to willfully damage my property I can sue you for damages. Equally if your child runs up to my dog and causes injury to my property that requires veterinary care, I can sue you for damages. Vet care is not cheap.