
Think under DDA, it has to be YOU that has reason to be afraid that YOU are going to attacked. There was a court case quite a while ago (not sure if it was DDA), but anyway, some dog had killed a cat & the cat's owner tried to get the dog destroyed. The judge threw it out because he said chasing cats was what dogs do.
However, if his Staffie isn't on a lead on a public highway, you could say he could be done for having a dog out of control. If his dog chased your cat onto a busy road, you could say if he caused an accident he could be liable for £100000 worht of damages - ask him if he has insurance. Can't you just sound as if you know what you're talking about & quote some legal-sounding gobbledegook at them, just so they know that you intend to take it further if something did happen? He can't be very intelligent if he does that kind of thing for amusement so he may well believe you!