It's very curious that the knob on the boiler returns to min.
Put a spot of tippex or something on the top when it is at min, then turn it up and observe what the spindle does.
Look for any maker and model names, or a dataplate that should be somewhere on the boiler and might be exposed dur to the missing lower cover.
Without the pipe thermometers it's difficult to know if the boiler is reaching overheat temp.
Turn the cylinder stat down by five degrees, and tomorrow see if it is still scalding. If you have a kitchen thermometer, take the temperature of the hot water.
Looking at your timer-programmer, in your latest photo the dial was between 2 and 3, so it should have been at the "2" setting (HW off) but through a little indicator window I see a number "3." This might be due to pressing the "Advance" button. Observe it and see if the number catches up with the timer next time the numbered tappets go round.
The whirring you can hear is probably the pump (dark red, two pipes, black label, probably marked "Grunfoss." The motorised valve (three pipes, square metal cover) can also whir, but only for a few seconds at a time. The pump should whir all the time the system is trying to heat either radiators or cylinder.
If you have a room thermometer, note the temperatures of the rooms when radiators are heating, and when off. Just in case there should be a concealed thermostat somewhere.
Look out for a grey or cream plastic box, about the size of a book, with several cables going into it. May be near the boiler.