Under section 22.3 of the Consumer Rights Act, and section 20, you have the right to reject the goods for a substantial fault within the first 30 days.
After 30 days, your remedy is compensation/damages which could be the value of the vehicle or the cost of a repair.
I don’t know whether you are outside that 30 day period or not.
However even if you are entitled to reject the goods and have a refund, actually getting out of the dealer, particularly a car dealer is going to be a job on its own because they do not routinely refund for defective vehicles, regardless of how major the fault is.
There may be an issue here with the RAC and the warranty because we don’t know why they will refuse to cover the cost.
However that’s between the dealer and the RAC, liability for this and having the goods provided of satisfactory quality, rests with the dealer.
If you paid extra for the warranty, you may be entitled to a full refund on that if it will not pay up.
The problem of course is that if they want refund you, you are going to have to take them to court.
Fortunately, you have the RAC report which is good evidence even though they are disputing it, it is likely that the court would believe the RAC report over any report prepared by the dealer who has a vested interest in saying that the RAC report is defective.
Can I clarify anything further for you?
Please rate the service positive. It doesn’t cost you anything but helps me greatly.
We can still exchange emails.