Many thanks to all who've contributed to this thread. I certainly have a better understanding of the set-up now, and in particular that there's no E7 or it's 3-phase equivalent in place.
I have yet to discover the purpose of the timer and associated switch, and what it actually switches. It may well be a legacy from when there was something like an E7 supply. Alternatively it may just be a precaution against leaving the NS heaters running 24/7. Without poking about and following the cables carefully (which is probably the job of a qualified electrician, which I am not), I may never know.
As for cheaper forms of heating and insulation, I have already had all the windows covered in bubble wrap, by way of poor man's double glazing. The are quite a few windows, single pane, quite high up, there is no view to miss, and they probably date from when the school-room was built (~1930). Winter will tell whether it actually makes any difference.
The two doors are in the process of being draught-proofed. Because they are old and warped, I've had to resort to 'Atomic Strip'
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I've had some in my bits-box for a long time (>25 yrs?), and quite glad to have eventually found a use for it. My parents house used it circa 1950 so it's been around for many decades.
We have considered dehumidifiers. They weren't going to be cheap to run at the best of times, but the recent price rises virtually rule out anything that uses other than the minimum amount of electricity. Anything like an air-sourced heat-pump is in the realms of fantasy, I'm afraid, even assuming the chapel would allow it to be fitted.
Thanks again to everyone.