The boiler man is here, and we need a new pump, as well as loads of other expensive-sounding parts.
Bollocks, I say.
Seems that the water pressure in the system had got low (which implies there is a leak which is worrying), so when the heating switched itself on in the morning, the pump seized and the boiler overheated.
So that explains the loud "Sproing" noise that woke me up in the wee small hours.
Arse AND bollocks, I say.