He appears to be charging £148 for the pcb + £148 for his time + VAT = £349.
It might take him an hour to obtain the pcb and, if he works slowly - an hour to fit it - so his hourly rate is £74 + VAT which is a little high - the pcb can be had for £149 + VAT from what I've seen on a web site.
Boiler pcbs probably cost less than £10 to make and usually sell for £100 plus - a spare-part scandal in my view but not uncommon with consumer electronics - think about it - you can buy a cheap PC for £300 and it's a lot more complex than a boiler pcb!
As for your particular fault - I'm nothing more than an unqualified muppet when it comes to boilers - it may well be caused by the pcb but I suspect that your man is just guessing as I am now - they get very well trained in gas safety and pipework etc but some are a bit weak with electronics.
It is possible and quite legal for you to replace the pcb yourself - but probably safer to have a specialist do it - try yellow pages.
The weak area of boiler PCBs is the odd dry joint but more particularly the Electrolytic Capacitors - they age in time and degrade with heat - and boilers are warm environments.
Good luck...
Peccavi, March 2010