Brian,
The common problem is the Thermostat (Boiler Temperature controller) and this is sometimes because of a faulty thermocouple which is the probe that actually measures the temperature of the main boiler heat exchanger. If faulty it could be kidding the thermostat that the temperature is higher than the trip temperature and hence the thermostat shuts off te gas. On most boilers the Thermostat provides an electrical signal to engage a solenoid in the main gas valve manifold. If the gas valve solenoid is not energised by the thermostat then the main gas burners will not be fed with gas to fire up. It is worth checking that your Thermostat is providing the gas valve solenoid with an energising signal with an electrical meter. Good luck and be careful.
John.
John Stokes, March 2005