Quick update.
She is not herself and lethargic for varying chunks of the day, but she is eating and scratching around. We cleaned her yesterday and today her backside was better with less poop on fewer rear feathers, but it was still there. So another clean and more Canestan. Her skin is quite red and irritated. Not broken skin but clearly red and splotchy.
Also, the vet called me last night to say the Baytril had arrived. I said that, having sought advice on here - and also hearing that not only in the UK but in the US as well, it is not licenced for laying hens )ie you can't eat the eggs after), I told we were not going for it. I also said that I thought (as I had done when I went in with Scarlett) that it was vent gleet. He then asked "what is that?" Now I don't think he's not a great vet, because he is, but he hadn't heard of it, which explains why he dismissed my suggestion of Canestan over a week ago and put Scarlett on antibiotics (which haven't done a thing other than mean we cannot eat her eggs for a fortnight). But he thanked me and said that it had given him something to research. Once again, I am not criticising him or doubting his ability, he has been marvellous to us and our girls for years, even operating on them from time to time. In British terms, "A good bloke".
Finally, just a quick question. Does vent gleet make some birds feel under the weather? Scarlett couldn't care less, whereas Betty is definitely not herself.