The symptoms that you are describing indicate that the secondary (domestic) plate heat exchanger is restricted with dirt in the primary water side (the central heating water section of it). This is holding back the heat in the main heat exchanger and causing the boiler to shut down on it's temperature control circuit.
To rectify the problem, the secondary heat exchanger needs to be removed and flushed out.
Although this will restore the boiler, it is very difficult to completely clean the heat exchanger. Moreover, the contamination came from the radiators in the first place, and as such the entire heating system will require chemical cleaning and re-inhibiting in order to prevent a re-occurance of the problem.
David Hickey, January 2007