Johny
Thanks for coming back and telling us a little bit more about the car and its history. Thanks also for calming down a bit and at least trying to make your story a bit more coherent. Having read it, though, I think you are a bit confused about the various different parties you are dealing with, and where their respective duties, rights and responsibilties start and finish. Hopefully, this will help.
First off, you bought the car from a private individual - your friend. That was a legal contract, and the contracting parties in that contract are you and your friend. As part of that contract, your friend also transferred over to you his rights and responsibilities under the warranty. The warranty itself is also a contract in its own right, and the contracting parties are the provider of cover and the owner of the car from time to time. I can't be certain without reading the warranty document who the provider of cover is but I would hazard a guess it is Audi UK. It is most definitely NOT an Audi dealer. Audi UK and Audi dealers are completely different commercial and legal entities. For the rest of this post, let us assume the provider of cover is Audi UK.
As I mentioned in an earlier post, both parties to a contract have obligations, and in the case of the warranty, one of the owner's obligations is to ensure the car is serviced in accordance with the specified schedule. You friend seemingly did not do that, so he was in breach of his obligations under the warranty contract. When he passed the warranty on to you, his breach became your breach. That might seem harsh, but it's how the law works.
To help owners comply with their obligation to ensure the car is serviced in accordance with the specified schedule, Audi UK provides the owner with precise and detailed information on what the schedule is; in the form of the service book. Owners should read it; it's important.
That brings me to the role of the dealer. Firstly, the dealer is not a party to the warranty contract. If a dealer carries out warranty work, it does so as agent of the provider of cover (Audi UK). The contract for warranty repair work is between the provider of cover and the car owner.
When a dealer carries out servicing work, it is not acting as an agent for Audi UK, it is acting for itself because the contract for servicing work is between the dealer and the car owner. The dealer's obligation under a contract for servicing is to carry out the work the owner instructs it to do, with skill and care and to a reasonable standard. It is not obliged to volunteer advice on what work should be done. Whilst it is good practice and good customer relations to do so, the dealer does not have a duty to do a customer's thinking for them.
If the customer asks for advice on what work needs to be done to ensure the servicing schedule is met (or indeed, if the dealer choose to volunteer it) it must give accurate advice. When you say your friend was never advised about when to get the gearbox serviced, well first of all he was, in the form of the information in the service book. As to whether the servicing dealer advised him, did he ask for advice? If he did not, then, as I said, the dealer was not obliged to advise him.
If a dealer does give advice (whether volunteered or on request), and it fails to give the right advice, then the owner may have cause for complaint against the dealer. But if the dealer's advice is faulty, and it leads to the owner breaching his warranty obligations, that has no impact on the position between the owner and Audi UK as provider of cover. Audi UK can still reasonably reject a claim. The owner would then have to argue that the dealer caused him to breach his warranty obligations, thus causing the claim to be rejected, and that the dealer should then stand in the shoes of Audi UK and fund the repairs itself.
To summarise your situation, based on my understanding of what you have told us so far, you have bought a car and extended warranty from someone who was in breach of his warranty obligations. That breach is now your breach. The breach may have been caused by negligent advice by a dealer to your friend, but even if it was, that has no bearing on the warranty provider's entitlement to refuse to meet the cost of repairs. If the dealer did give servicing advice that was negligent, that advice was not given to you. It was given to your friend.
I'm not an expert on the law, contract or otherwise, but the way I see it, your remedy for being unable to make a claim on your warranty is to sue your friend for concealing from you his breach of the warranty terms. He, in turn would then have to sue the dealer for giving him negligent advice (presuming it did do so) that caused him to breach the warranty terms.
For all sorts of reasons I can see that you would not want to do that, so the only real alternative is, as has been suggested by others, is to ask either Audi UK or an Audi dealer to help out on a goodwill basis. But like everyone says, be nice.
If anyone reading this is an expert on the law, and identifies mistakes on my part, I am happy for them to be corrected.