The next thing planned was to move the boiler from its current position (outside wall of the garage) to the kitchen, on the new wall that's blocking the usable bit of kitchen off from the shortly-to-vanish bit. Our builder had arranged for a gas engineer to show up yesterday evening to do that.
We'd noticed a bit of dampness under the boiler while clearing out the garage, but had thought it might be one of the taps nearby that was causing it. Sadly not; the gas engineer's opinion was not so much "where do you want this moved to?" as "this thing is leaking like a sieve! See how I condemn it. I'm not moving that thing anywhere, except maybe into that skip over there." (Bloody thing can only have been about six or seven years old.)
Luckily, our hot water tank has an immersion heater built into it as a backup for this sort of emergency. We switched that on last night.
Even more luckily, rotwang checked if it had worked before he stepped into the shower -- as it hadn't.
I asked the builder to take a look at it this morning, and we found out that: (a) the fuse from the immersion heater switch was missing (why?), (b) in any case, the switch itself was also todgered. Asking the property's former owners: "oh, yes, that never worked, did it?" (i.e. it has been broken for at least 12 years)
Replacing that appears to have got us hot water, at least, though of course it won't help with the central heating; fingers crossed for a mild autumn (we reckon it'll be about six weeks before we're at the point where we can put a new boiler in).