The vet on Monday thinks it's either spay incontinence or diabetes insipidus, so Dr Google (DVM) was on the mark

He gave us some tablets (
Incurin) which contain a short-acting estrogen, for the treatment of spay incontinence; if they work, that's what it is, otherwise we'd try the treatment for DI. She started them on Tuesday and has been dry since. That seems very quick, but I'll take it, as she was having an accident at least once a day before we started.
We have a month's supply, so we'll see how she gets on.
I just read the data sheet and it says I should be very careful handling them and wash my hands thoroughly with soapy water after administration. Whoops!