Thanks ProfJohnL. In answer to your points:
1. This could be the reason because although the battery is relatively new, it lost a lot of amps in the four weeks between Easter and May Day B/H - from 14.4 down to single digits. But doesn't being on EHU negate the battery issue? I've no idea.
2. I have thought about trying another pump and will be doing this soon.
3. I haven't checked the owner's manual, stupidly, but have nevertheless followed verbal instructions from a caravan dealer as to how to set it. I'll have to turn the knob both ways again but - when the water flows through the taps ok - I'm never sure where to leave it!
4. Yes, I've ensured the yellow drain valve by the boiler is in the up position.
Many thanks for these points, I will go through them next time!