I'm no Lawyer, but here's how mine was rejected with the minimum amount of stress. The following plan was stuck to with military precision
1. First and foremost, keep a diary of every fault, every time it happened, and the circumstances in which it did. Keep smiling, be polite, NEVER show your anger. ALWAYS show how hurt you are!
2. In your diary, keep an
exact record of
every conversation/email/letter with your dealer/dealers AND the finance company (if one was involved).
3. Let your dealer know that you have, and will continue to keep, an exact record of everything (all of the above). Conversationally something like, "I started recording everything from the start, because I thought it'll help you guys if
you have to try for a refund from MINI - just ask if you want it to send to them, I'll help you all I can...." Smarmy as hell, but works.
4. Let your dealer know that you are unhappy BUT that you are happy to work to the best solution for you both - at the same time make sure they know that YOU know that this is between you and the dealer, NOT MINI!!!!!
Whilst you don't
have to work to fix it with them, the idea is that
they think you are extremely reasonable - but that you are well informed and very calm BUT, that you are
completely determined ('nicely evil' is good), ALSO, it helps to have friendly conversations with the service manager (you need him onside) and preferably the sales manager too. They are the ones that will give MINI an ear bashing because they'll know you're determined. I used these conversations to drop hints like, "I'm surprised there's still a Puma out for this, this faults all over the Internet. Even Youtube. Haven't you seen it? Oh, well here's the link".
5. In all of your dealings, voice your disappointment with the
buying and owning experience. This is
extremely important - MINI sell the car on emotion very heavily, it's this that you're aiming at.
6. All of the above is your game plan for what you know you are going to do eventually SO, now you document all of the last few months crappola and serve it to them very politely. At this point I made it clear that I will be happy to have another MINI to the same value.
7. At the point you offically reject with the dealer (now in writing), ASK THEM if they would prefer to deal with you from now on - or your solicitor. They won't want to deal with your solicitor......
All of the above related to undisputed evidence (engine rattle recorded on disc, compared to normal start-up), so think about how you can 'keep evidence' on record. It would be really bad if these faults were
really over Youtube like a rash wouldn't it?
Remember. Don't get mad, get even, and showing your anger will alienate the dealer - then it's harder work!
Oh, just so you're not surprised, they don't like the word 'reject'. I got used to saying I'd like the car 'substituted' or 'exchanged' for another with no faults.
Good luck Dan - I'm now the proud owner of a six month newer car, to a spec I
much prefer.

Hope you get it sorted.