Thank you very much, James.
I am still hopeful someone might know what kind of water system we have at RQ, please, as between e.g. low pressure gravity, mains pressure combination boiler, mains pressure unvented, or even 'cold mains'…? I freely admit I do not know and realise I have not had any particular reason to know until now.
It sounds like in your case the plumber managed to track down a Bramham shower cartridge/valve spare part. I have come across them in my search, and they do indeed retail around the £250 mark, which also seems to be the average price of a half-decent new shower, so that is where I am currently looking.