You have a contract for the used car. The dealer is in breach. He needs to pay you compensation, for the inconvenience of not having the car a expected, and if you find a similar car for any extra cost that may be.
I suppose if they offer to provide you a car until when they find a similar car and supply that similar car for the same cost then that should be ok . You should be at least expecting something similar.
In any event, this is disgraceful service form a maion dealer. At the very least they should be apoogetic, admitiing it is their fault and explaining what they will do to put matter right.
They are in the wrong and not you.
I would write a letter to their head office sayijng that you expect thing sorted or if not you will be resorting to legal action.
As I say it is a clear case of breach of con tract, (unless te terms of the contract say something differrnet and the term isn't unfair. - if they made a mistake tough luck.
Write to Audi UK and What Car? if they don't sort it out.