Ideal Concorde thermostat problem?

I have a very big, very old Ideal Concorde 2a boiler (it runs 21 radiators!)
Problem is it is too good!
The radiators, when on, would become very hot indeed, and the hot water at the tap was almost scalding. Turning the thormostat knob on the boiler made no difference, it's either off or very much on.
So ... I bought a new thermostat to solve the problem. Eventually sourced the correct item, fitted it, and lo and behold ... the problem is still there. Exactly the same.
Apart from the obvious new replacement boiler, can anyone offer a simple suggestion? If its not the boiler thermosat, what can it be? We have no room thermosats, only adjustable thermostatic controls on the rads. Many thanks