According to the orriginal post the dog ran out from the garden onto the street and attacked his dog. Clear and Simple, it was not on private property-- Dangerously out of control in a public place-- Dangerous Dogs Act 1991.
I have successfully prosecuted people for similiar offences and there are other bits of legislation that can be used including the Road Traffic Act as it is the owners responsibilty to ensure that animals are prevented from straying onto highways and causing a danger to highway users.
I am not a solicitor, but when I worked for local authority my position was Enforcement officer for all dog related offences. I used to investigate each case, gather the evidence and produce the prosecution files, for which I had to have specialst trianing. Contact Plod and your local dog warden, the least that should be done is for your costs to be covered and possibly a Home Office Caution.
Ade