I think I may have diagnosed it - I hadn't noticed until I was just leaving, but the thermostat unit is wireless, and there is a receiver on the wall next to the boiler (really high up, so it wasn't in my normal sightline). There is a little light on the receiver, next to the word 'on', but the light isn't on. So I think maybe the receiver isn't picking up the signal. I can't be sure, because I've never noticed the receiver before, or if the little light was on. Annoyingly the reciever doesn't have a nice clear On/Off or Reset button. I've googled, and got something on DIYnot.com, about reintroducing the thermostat and reciever, but I'm loathe to muck about myself, as it's not my system. The owner is back tomorrow, and probably better able to work it out (or will know where the instruction manual is).
The pilot light must be ok, because the boiler comes on and heats water for the tap... So it's not leaking unlit gas or anything.