I guess it also helps that you spent £70,000 odd on an Audi R8 from them whilst having also been a customer of theirs on other high end Audi's in the past...
Unfortunately, used car dealers are masters of shunning their responsibilities. These days, the tactic they seem to use is that they sell the car with some utterly useless warranty - then when the customer complains days/weeks later, the dealer says "Oh no, that sounds awful - be sure to contact the warranty company about that" knowing full well that the warranty company will reject the claim and allowing the dealer to wash their hands of it, blaming the horrible warranty company.
They can cram all of that up their backsides. They sold you the car. The responsibility lies with
them to rectify the fault or give your money back. Do not pay money towards getting it diagnosed, or go 50/50 on things, or any other concoction of deals they want to work out with you - this is their responsibility to fix, end of.