The solenoid coil of the cold water inlet valve has gone open circuit. Not bad given its age, but the shower is a tall narrow unit in an enameled steel cabinet so fitting a modern short wide shower would take some work.
I'm wondering what the chances might be of finding a replacement solenoid. (Not even 'slim to none', do I hear someone say?)
It's a Redring 'Leisure' 7KW shower, model 53-767001 according to the label, and the solenoid itself is labelled 'Eaton' 2/100 N/cm2 220-240V 50 Hz 6VA Tm 25C Tu 60C KEMA EUR S, 631/0 S 6 60 Hz UL B147 which is maybe not very helpful because none of that looks like a part number. The cylindrical coil is separate from the actual water valve and is potted in some green compund so not easy to repair. Unless of course the fault is near the connector tags - maybe I should try to find out.