I had similar issues but a long time ago so things may have changed.

Yes to keeping records of anything and everything.

The comment about an inspection is important. Unless you are a fully qualified motor vehicle engineer your view on faults if pretty much worthless when push comes to shove. However, that inspection report is effectively an "expert witness report" in the same way that a forensic report is used when prosecuting criminals. Unless challenged it provides solid evidence about the state of the car, faults and all.

That is what you use to go to (1) the selling dealer (2) the group head office (3) Audi UK, Trading Standards and potentially Court etc. etc, to make your point and show that the goods are defective and you are rejecting them. Particularly if there are areas/issues which are stated/claimed have been done, and haven't - as shown, detailed and described by the "expert" in the report.

Good Luck.

Andy.

PS I will never understand what motivates dealers to act this way as the negative publicity will certainly cost more than the repairs. I, for one, will never own another car of the marque involved all those years ago and AFAIK none of my family/friends/colleagues etc that know what happened have done either.