So, everything is in - and then we discover that the cold water tank is only about 6 inches above the shower head, the pressure is near zero, and thus the thermostatic valve is shutting the shower off all the time because the hot water pressure is massively higher than the cold.
The plumbers couldn't believe we were still using a cold tank when there's no hot tank any more. The previous people had the hot tank replaced with a combi boiler, but didn't get it followed through. It'd cost a grand to actually get it all ripped out and replastered - so that's a job for next year. Fortunately it'll only cost £120 to put in a bypass, so they're going to do that next week, at which point I'll have decent pressure through the whole flat, which will be lovely. And we'll finally be able to have the shower I've been looking forward to for two weeks.
(Don't panic - old shower room still works, so I can stay clean until then.)