To all those saying that the rabbit should have been in a fox proof run, or that the fence might be too low, or in disrepair, the law in UK says that as a dog owner you are responsible to keep your dog under control. It is up to you to keep your fences in good order, and to prevent your dog from doing damage.
The rabiit's owner would be responsible if she/he had let the rabbit get into your garden, then you wouldn't be liable, as your dog was secure in your garden.
Cat's are not viewed in the same way under law, so if the nieghbours cat had attacked the rabbit, then the rabbit owner has no comeback.
For example, we have chickens who free range. Our garden as it happens is very secure. If I let my chickens out and a fox gets them, that is my tough luck. If one of the neighbours' cats catching one, it is my bad luck. If my neighbour's dog gets under the fence and gets one of my chickens, then it the neighbours responsibility.
I know I have been one of the ones talking about the vet's bill etc, but I have said very clearly all along, that the OP is liable.