Wow, what a load of moaning old ladies

My take:
Morally, there is a case for reimbursing the vet for his help in trying to save your beloved cat. If he'd succeeded you'd probably be very grateful indeed etc etc. Equally you could say that morally the vet should see how skint you are and not charge you for helping an animal in pain.
Realistically though, trying to remain objective for the sake of discussion, I agree with Scuzi et al. There was no contract formed (as per Consumer Credit Act) and no agreement or obligation to pay was arranged. If I had a cat and it got run over, I'd shoot it and bury it and it'd cost me about 2p; the fact the vet
took it upon himself to decide he was going to try to save the cat and treat it was HIS decision.
To contact you out of the blue and demand funds is dodgy indeed. At best, he should have said "Hi, your cat was brought in injured on xx date xx and we saw s/he was in pain. You couldn't be contacted so we decided to try to save the cat, but sadly failed. It cost us £xx (actual cost not vets fees cost) to do so, we would be grateful for a voluntary contribution towards offsetting this."
We had an incident years ago with one of my dogs. He sliced an artery and peed blood for nearly an hour. A kind stranger stopped her car (I was 17) and offered to drive us to the only vets open on that Sunday - 30 miles away. All local practices deferred emergency care to this one clinic for Sundays.
I explained that I was only 17, hadn't much money (and certainly none on me at the time!) and that if I could afford treatment I'd pay. If not I'd put him down. They said it'd be around £250 but I could pay in installments, which was very nice of them. Nothing was signed. A WEEK after his op (he was fine btw) a large black guy hammered on my mum's door, pushed his way into the house and said if she didn't pay £500 there and then for the vets fees, he was going to start "helping himself.
She naturally cacked herself, and phoned the police. We spoke with a solicitor about it and he sent one paragraph to the vet's office which said something very much like:
"Dear sirs,
Reference the intimidating gentleman you dispatched to speak to my client's mother on xxdatexx. Please forward a copy of the agreement my client signed under the Consumer Credit Act. If you do not have any such agreement, feel free to never contact my client again."
They wrote back next day waiving all charges and fees, and that was that.