UPDATE: The shower just cut out again. This time without any kettle being boiled, so no extra electrical load or any taps running.
I guess it means the shower is at fault (in winter of course, just after the old boiler packing up in late February!).
So what do I do now, replace the shower or try a cheap repair of some kind (thermal cut-out?).
Ideally I'd drop the electric shower and run one of the new combi-boiler. But the complication is, the bath taps are at the other end, so there is not any hot water pipe right where the shower currently is, and it does not look like there is enough space to bring a pipe up on this side of the bath (the electric shower's cold feed appears in the middle of the back wall out of tiles). The other side of the bath is not against a wall but there is a boxed-in section of about 35cms to the outside wall (and a window). I could perhaps install the shower on the side wall, but then I don't know what to do for a bath shower screen (is there such a thing as a big L running across the bath and then she side of the tub facing the room??). Or I'd need to move/change the bathtub towards the outside wall with the window, but this would be a major job which wouldn't want to attempt by myself. Getting someone in for this would be difficult on short notice I guess (now lockdown, soon tier 3)...