So last night was the first time the central heating was on for ages. And it didn't work.
The boiler went on ok (it does hot water too, so gets used once or twice a day), the pipes near the boiler got hot, and the pump got decidedly hot. But the radiators didn't.
Apparently, this is a Known Problem in such circumstances. Bits of sludge collect in the pump over the months and it has problems starting up. (Modern pumps run for a few seconds every day, even when the heating's off, to avoid this.)
When it happens again in a year's time, the cure for our system is to use a coin to take the big screw cover off the front (with a tray underneath, because there will be drips) and use a screwdriver to turn the pump's propeller a little. Put the cover back and try again. The movement you did should have cleared enough for it to start... if not, use the switch underneath the pump to set it to III (max power) rather than I (enough power normally).