I think Kevin's contribution is another question rather than an answer for you.
I have a prejudice that boiler engineers (Gas Safe in the UK) as a group - tend to lack diagnostic skills they may be OK with issues of safety but too many of them tend to guess and swap out parts willy-nilly at the customer's expense.
Gas Valve and a circuit board replaced? At the same time? The engineer is taking advantage of you - it would be a remarkable coincidence for both of them to have failed at the same time - he will have your "broken" items as spares in the back of his van.
Contact trading standards and make a fuss - complain to the scallywag who charged you £350 - ask for your money back.
Seek out an alternative and different engineer - challenge him to fix your problem as cheaply as possible - do not accept the excuse - "it's gone I'm afraid lady."
Ask what has "gone" what is wrong with what - how does he know? What if he's wrong?
I do not know boilers very well - no skills or experience. If the boiler runs for a short tie and then cuts out i would suspect that it's overheating or that it thinks it's overheating. That would suggest the pump not moving the heated water away -or- the overheat cut-out operating prematurely.
A competent engineer 'should' be able to make a quick and accurate diagnosis - a cowboy will just change things on spec.
Do not let the boiler-man intimidate you - if you're unhappy with his work tell him so and withold payment until you get satisfaction and some heating.
Good luck...
Peccavi
December 2012
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