There should be a fused switch somewhere that provides power to the boiler circuit. This will provide power to the timer, boiler and external pump. The timer will switch on at the predetermined time (or permanently is set to do so). The thermostat will decide if there is a demand for heat and switch the power on to the boiler and pump.
By turning the boiler off you are only turning off the burner, not necessarily the pump, which is being controlled by the timer/stat.
To turn the heating off completely you will need to find the fused switch.
Now, from what you’re saying, it could be a faulty programmer that is permanently on. However, if the rads are extremely hot then it could be a thermostat problem, though it doesn’t account for why the boiler doesn’t switch off.
Another thought – is your hot water programmed to stay on all day? If so, you may have the motorized valve that switches off the central heating flow stuck open. In this case the stat will have no effect as demand is being dictated by the temperature of the hot water cylinder.
Central heating systems are many and varied are the ways to wire them. It’s difficult to say without seeing it.
If you’re in Pembrokeshire I’ll come and have a look.
Rich.