When I was in your position I had adjudicator ruling in my favour but the dealership involved either didn't have a clue about what that meant or were still trying it on. With an adjudicator ruling in your favour (and short of them appealing it to the ombudsman) you are almost there. With mine they finally realised that I would take them to court for enforcement and they sent me a letter offing to settle in line with the terms from the Ombudsman. At this point you are in the driving seat - they included a confidentiality/non-disclosure clause in the agreement - I made them pay for that - I also sought additional compensation above and beyond that determined by the ombudsman. They at this point want to settle without compromise for them (i.e. getting a court enforcement against them or having me blab on appropriate forums etc) so you are now better placed to dictate those terms.. My quest took best part of a year but I now have the signed settlement letter framed in my office.

Buy you out means they will after to buy it back at below what you paid (probably) or offer you a replacement vehicle but ask you to make a contribution. If they have documented engine failed - needs replacing they either do that, replace like for like (whole vehicle) at no cost or refund you in full - iIn fact IIRC if they can't repair it YOU chose replacement or refund - not them.

Is it a Cooper S? Have experience of someone rejecting a similar car due to dealer not being able to repair noise of deal with 'excessive' oil consumption + as few other issues - given them the opportunity to fix it (you have to) if it is not resolved to your satisfaction then reject it. Expect them to refuse - if you are lucky you brought in on finance so can reject it to the finance company - they will refuse it as well. Then complain the financial ombudsman about the finance company and assuming that you have a genuine fault that hasn't been repair they would support you rejection and the finance company has to pay out. No one accepts liability until forced - you have to see it through

take the above users advice and go to small claims for the difference - you have been stitched. Evans Halshaw - part of Pendragon - it appears to me that they play a numbers game with customers - i.e. some of them go away and some they have to pay out. I stuck it out and got a full refund + interest Stick it to them ...

did you agree to buy the new vehicle based on the offer of £6,000 for your old one?how did you pay?If your decision to buy the new vehicle was based on the offer the dealer made to pay you £6,000 tradin then you should at least be able to back out of the whole deal. Did you get any paperwork?

sometimes I do wonder what bunch of jokers advise some of these companies....

Yes they are - the situation you talked about sounded just like something they would do!

Is this an Evans Halshaw dealership? only this have some overtones that sound familier to my case.

thats good - I'm all up for seeing the consumer do well in a deal but be sure most vehicle retailers have a finely honed legal arm!

Interesting what you are saying is that once they settled your outstanding finance you want to then just discontinue your agreement to buy a new vehicle? Although the paperwork might not indicate the deals are linked there would be a fair chance that the dealership would look to prove that they were indeed joined - "we agreed to buy and settle your car AND you agreed to buy a new one from us..." - should they choose to get litigious about it then its your word vs. their word on what was/wasn't agreed and if I was the judge I think I'd find in favour of the garage. Risky... and as previously pointed out you'll get more money on your car from doing a small bit of leg work.