Firebird Popular 90 - Thermostat doesn't seem to be working

Yes, its preset to operate, I think, at between 110C/113C, Have you got a open vented system with a feed & expansion cistern (small "tank") in the attic or a pressurized system with a expansion vessel, if open vented then very hot water might start circulating around the cistern and if plastic, it might rupture with dire consequences, my advice is to shut down the boiler and get a competent person to inspect/fix it.

Just to be clear, is the burner firing continuously without cut out??

How many rads have you got, double/single??

Edit: I see you are "controlling" it with a timer, very dangerous because if the circ pump stops (and it might fail at these very high temperatures) then you will immediately start generating steam at the rate of ~ 32kgs/hr.

can you post a pic of the stat as some old stats didnt have a high limit back up

Its more than likely thats the one you have because the single stat doesn't have a reset button?.

combine this with :
" As I mentioned in all my years in the house I have only ever used the thermostat in the living room to set temp and even turn off the heating (if you know what i mean) so never had to use or bother about the thermostat located on the boiler itself."

" The electrician laid near wiring down the side of the garage across the footpath to the boiler house however in doing so the thermostat mounted on the living room wall is redundant. "

Why/how roomstat was made redundant ? was boilerstat made redundant same time?

"The boiler thermostat is kind of stand alone - It is wired to mains and then this is fed to the Rielo burner, right?"
No, it has to operate in conjunction to your heating control system. Same apply to your roomstat and Hwaterstat(if present), circulating pump(s)

What heating system controls you have? How do you turn your heating/Hwater ON?
Burner have to be wired into that system to start on heat demand and turn off when no longer needed.

I have sunvic controller and motor valves(rads/Hwater) that start boiler once activated(preset timer or on demand).
Boilerstat , from images, looks untouched wires .
If roomstat no longer operational, might be some wiring changes were done at controller side or junction box . Live vs switched live, etc
Where does boiler stat connect to? 3pin plug socket or junction box, because, i assume, wiring replaced from there to the house(controller/junction), right?

Another thing to check - temp knob on boiler stat might be damaged/disintegrated and no longer turn actuator - lift it, observe internal mounting latch. you should be able to adjust setting with pliers if knob is broken