millizoe trying getting your facts right before you answer, gas engineers now have to register with gas safe but Corgi still exists, membership is now voluntary and I can assure you they do more to ensure the safety of gas use than Gas Safe do who only exist to take money and offer little in return compared. Did you also know that Corgi was originally a charity set up by British Gas to promote gas safety whereas Gas Safe is run by a private profit making firm.
is your heating system sealed in that there is no header tank in the loft and there is an expansion vessel and pressure guage somewhere or is it a conventional open vented system with a header tank?
sounds to me as though it's a circulation problem i.e. the water in the system is not flowing through the boiler quickly enough and is getting too hot within the boiler and thus cutting off on the safety stats before the rads can get warm.
could be caused by the pump as already said although i would have thought the problem would happen on hot water too ( is the pump set to the right speed ) could also be caused by air in the system, could still be sludge if it wasn't flushed properly, could be a dry header tank if it is an open-vented system or it could be the 3 way valve presuming you have a common y plan system.
as for the turning on the rads one at a time if you have thermostatic rad valves and you turn too many off then this can also cause poor circulation and overheating at the boiler. May also need to check any manual or auto bypass is open.