It appears the one of the powered valves that governs whether hot water flows into the radiators had siezed, and if that valve doesn't open, the central heating pump and boiler don't get turned on either, which is why it's all been sat there doing nothing. Not something I would have worked out for myself, so I don't feel too incompetent for not having been able to diagnose it :)
Everything appears to be warming up, so all I need to do now is bleed the radiators when I get home from work and it should all be good.
