Quite likely to be a jammed heating pump. This happens to us every autumn, because I always forget to run up the heating a few times over the summer...
However, it's easy to fix.
Turn the heating off first, and identify which is the heating pump (if the heating's been turned on, you'll find the jammed heating pump will be at least as hot as the boiler pump, so you can't just tell them by temperature).
If you have the usual Grundfos pump (maroon Hammerite), on the flat side you'll see a circular silver nut with a screwdriver slot in it. Unscrew this, catching the drips -- careful not to lose the rubber seal on its edge. This exposes the end of the pump spindle. Use a screwdriver to turn the spindle a bit. Presumably other makes of pump have something similar.
Turn the heating on before putting the nut back, and you should be able to see the spindle going -- it'll drip a lot more too. Be very careful indeed not to get water anywhere near the electrics. Turn it off again and replace the nut with its seal.
If you're unlucky, the pump will have burnt out and you'll need a new one. Easy to change though. If the plumber remembered to put a gate valve either side of the pump you won't even have to drain it down.