Expanding on the above a bit, assuming your system is anything like conventional, your controls (programmer, thermostats, etc) operate one or more electrically powered valves in your heating pipework. They do not control the boiler or pump directly.
The valves each contain a switch and it is this which controls the pump and boiler, so if the valve malfunctions it is possible for the boiler to be permanently on, or permanently off, whatever the programmer, etc are indicating.
The valves have a manual over ride lever on the side of the head, and moving this to the full 'on' position then releasing it to return on its spring can also sometimes dislodge a stuck switch.
Note that the 'head' of the valve can be replaced separately from the valve part.
P.S. Just noticed where you live. It's possible that there's a frost thermostat connected to your system, to prevent any chance of the water in the pipework or boiler from freezing. If so, it may just be doing its job, wit nothing wrong.