Matt.
It is evident from what you described that the valve body fault was introduced while the car was under repair. To my mind that makes the garage that did the work responsible for putting it right, however it will undoubtedly argue that it was co-incidence or an existing fault, and hence will deny liability. It's going to be tough proving the dealer's responsibility, and given that the repair cost is going to be £5500 it may need to go to court for a settlement. It is certainly worth appealing to Audi UK, but I would simultaneously consult a solicitor for advice on your options and your chances of winning.
Whichever route you take to resolve the problem is going to take a long time. Months or possibly years in fact. If you want the car repaired now you may well have to pay for the work in the hope of recovering your costs at a later date. That is a choice only you can make.
Sorry to be so pessimistic. Justice does not always prevail.