My radiators are hot when the thermostat is switched off - would this be a problem with the thermostat or something else?

I can only turn the heating off, on the main switch on the boiler - as the hot water and heating are two separate switches

The radiators will stay hot for a long time with the thermostat off. You could have a pump controlled system or a valve controlled system so you might have to see if the controller or pump/valve is defective causing the boiler to run all the time. Boilers can be a pain to work on if you have no experience I suggest you call for a ON SITE inspection and repair from a professional HVAC person.