If the 'Boiler On' light is not lit when the problem occurs, that suggests that the thermostats and motorised valves are working and turning off the control signal to run the boiler.
If you want to be absolutely sure, as a test, you could install a switch in the wire going into the boiler 'switched live' terminal (the far right terminal next to the thermostat knob) leave the switch in the 'on' position and run the boiler as normal. When the fault occurs, operate the switch. Does the boiler stop? if so, it is something outside of the boiler that is causing the problem (thermostat or motorised valve). If it continues to run, something inside the boiler is at fault. After that, it may take someone who has a good working knowledge of circuits and a multimeter to find the actual fault, but this should narrow it down a bit.
If you want to be absolutely sure, as a test, you could install a switch in the wire going into the boiler 'switched live' terminal (the far right terminal next to the thermostat knob) leave the switch in the 'on' position and run the boiler as normal. When the fault occurs, operate the switch. Does the boiler stop? if so, it is something outside of the boiler that is causing the problem (thermostat or motorised valve). If it continues to run, something inside the boiler is at fault. After that, it may take someone who has a good working knowledge of circuits and a multimeter to find the actual fault, but this should narrow it down a bit.