Wow! I'm having exactly the same problem, and still waiting for an answer!!
I have a Glow-worm Space Saver 40B Mk 11.
I've replaced the thermocouple, thermocouple conector lead, pilot burner and the gas valve. I'm just about to replace the thermostat.
From cold this morning, the boiler ran for a good half an hour, BUT with the thermostat on the very lowest setting. Once I turned the thermostat up (ever so slightly) the problem reoccured.
I tried it on MIN again, but as the boiler was already hot, it only ran for about two minutes, and then the burner and pilot went out.
Sometimes, it will run for longer, but eventually cuts out. The flue is clear and the pump is running. I have also drained, flushed and de-sludged the whole system!
RSD, November 2006