Thanks to the people who sent messages and said little cat-sized prayers.
The vet gave her antibiotics, IV drips of saline, glucose, vitamins and other kinds of super-nutrient supplements. He gave me special food for her, and at first it was a bit of a struggle to get her to eat it. But now she's just yumming it all down. We went back tonight for a follow-up and she's strong enough now for the next stage in the special diet. We've moved from "recovery" diet, to "renal" diet, which she will have to have for the rest of her wee life. But it's not going to break the bank. And neither is the vet bill, because... Norcia! where things are just... well... sensible.