Apparently what was wrong with the boiler was exactly what we'd thought - the device that determines that both gas and water are present was all blocked up with dirt, so it kept on thinking that one or both of those were missing, and activating the safety cutout. It was quick and easy to get fixed. However, our boiler is still 12 years old, and a cheap, nasty model from a cheap, nasty brand. So we still need to get it changed as soon as possible, because it's going to die completely, soon. Been given a quote for replacing it with a lovely, shiny, good-quality energy efficient new boiler, which seems reasonable - except they'll need physical access to all of our radiators. The house is a fecking tip right now, so this is going to require that spoons are spent in tidying up. Eurgh.
One of the things I didn't mention in my last post was that not only was it taking me 40 minutes to get enough hot water for a bath, but I was having to carry the water upstairs in buckets. Couldn't get hot water out of the upstairs taps at all, and I had to be downstairs so that I could keep hitting & resetting the boiler. Ewww. Now otterylexa & I have both had showers and feel a lot happier about the situation.
I am very grateful to Alexa for having been here helping to keep me sane, because I don't think I'd have managed to get things sorted without the support.