I am definitely an idiot... There was a thermostat tucked away that I hadn't come across yet, and that was turned down too low for the pump to come on...
Thank you for all your help though!
We have a gas boiler downstairs by the programmer, but the pump is upstairs by a water tank with what looks to me like an immersion heater. Does that make sense?
I probably wont try unscrewing that thing just yet, especially as the pump has been fitted with all the electrics at the bottom!
I moved into a new place in the summer, and haven't been able to get the central heating going properly since I first tried turning it on a couple of days ago.
I should confess to being pretty clueless on these matters, so I'm adding a picture of the pump setup.
All the radiators are...