If at any point in this process the selling garage gives you the opportunity to hand it back and walk away with a reasonable percentage of your money back, bite their hand off.
It doesn't matter how pretty it is, this car is seriously not worth the hassle.
I fear we may all be too late, as it seems the diagnosis and repair was done before we heard about it on here.
If I've followed the thread correctly, the repairer is not the seller.
If this is correct, once another repairer has touched it, there will be no redress against the seller, as they will point out that they have not had the opportunity to fix it earlier, and now someone else has worked on it it is difficult to apportion blame for any subsequent faults.
Check the small print of the warranty carefully. Some may state that the warranty is invalidated if repairs are carried out other than through the selling dealer.
However, you also have the protection of the Consumer Rights Act 2015 and these rights cannot be overridden by the terms of any warranty. If a serious fault develops in the first six months, and that fault was present at the time of original purchase, then you may still have a claim against the selling dealer. Crucially, in that six month period, there is an implied assumption that the fault was present at the time of purchase; the burden of proof to show otherwise rests with the seller, not you.
Your local CAB may be able to help.
If you paid any part of the purchase price on finance, or with a credit card, then the organisation providing the funds will also be jointly liable.
If you want to read another story about someone who was sold a 500 which turned out to be a lemon, have a read of
this thread. Fortunately this one had a happy ending.