I cannot help with the legal side of this, but I will give you my personal advice, as you may find it useful.
- Her dog, should not be wondering around the public streets without a lead, which of course means the russel's owner should be present. The woman in question, is to say the least, lazy for not walking her dog proper, because if she did so, it would not need to be wondering the streets for excersie. Report this woman to the council, probally the dog section would be the best option, and maybe to enviromental health as no doubt it has made a "mess" on the streets, and not been cleared, which is a offence. usually a fine is the proposed penalty. Refuse absolute point blank to pay the amount of which she is asking as HER dog came onto YOUR property and it was something which dogs do, (play, get excited, sometimes minor injurys do occur, although it does seem this little dog was unfortunate.)
Let us know the outcome please!!