I notice in the description you say the the engineer that shut the boiler down took pictures and carried out a report. First off did he leave a warning notice and put a sticker on the boiler,regarding leakage of fumes, this is known as Spillage and if this is occuring there should be visible signs on the flue itself, boiler or flue joints. These will take the form of staining or black sooty marks which come off if you dampen your hand when touch them and then have to result to having to wash hands in soap to remove stains.
If there are no visible signs of spillage, then the engineer may have shut the boiler down on the basis he assumes the construction of the the flue to be incorrect and as such may be spilling P.O.Cs, Products of Combustion.[CARBON MONOXIDE] into the loft area.
As you have not put up any pics this is more difficult,however from what you say from the break down history,fitting all these new parts with big waiting times in between,still not working and discovering the Flue at fault,tells me only one thing The previous engineers had nt a clue what was wrong with your boiler and just kept throwing parts at at it until it worked.
Regarding can you do anything about this. The regulations are very strict on this.
If any Gas Safe Registered company as it is now,or Corgi as it was then,installs a flue incorrectly,or not fit for purpose and then at a later date is deemed to be unsafe, due unsatisfactory materials or poor workmanship then the Company in ? could find themselves in big trouble, if not already,provided a R.I.D.D.O.R has been raised against them.
You are in a good position here, if the company in ? and provided they still trading.I think you will find they ll be very keen to rectify the situation at No Cost.
If by now they have nt contacted you thats very un professional. Then contact them again by E mail informing them unless they discuss this matter,then they have you put in position with no option to contact Gas Safe Register for an Independant Survey. [which is free]. Which should wake them up a bit.. I hope this helps.

I would be interested to know what make & model of boiler you have in the the loft,you can PM me..
Cheers John..