In USA there are clear “lemon law” guidelines for what happens when a car has repeated problems. I thankfully have no experience with the law but my understanding is that the law does work … in England there is no direct equivalent that I know of; the closest would be the “Sale Of Goods” act which requires that something be “fit for the purpose for which it was sold”.
There is a sorry tale on MINI2 at the moment of a new MINI Convertible with repeated failures; the owner (convertible) writes “The problems started with the roof failing during the handover which delayed the car’s delivery by a few days until it was supposedly “fixed”” … “waited 6 months to take delivery and it is the worst car that I have ever had” … and he has posted this picture:
It seems there are “teething troubles” with some of the early convertibles; for the good of the customer and the good name of MINI, dealers should be striving to resolve these issues and work with the customer, and not fight against him/her.
UPDATE: The owner, Darren, sent me a video of the convertible roof (not) working; it does not look well:
M&I / GBMINI 
Comment on Lemon Laws…Here in CA it is very hard to get the dealers to do anything having to do with the “Lemon Law”. I have a friend that had one of the 1st new Cherokees back in the ’80’s. It took him a year, and much expense, to get them to replace the vehicle which repeatedly would stop running on the freeway and was burning a quart of oil a day with some 5000 miles on it. he finally garaged it for a year until it was resolved. CA was not very helpful.
Wow, that poor soul with that cab. Ian there are few dealers, like yours, that have any sort of scrupples. As we found out when buying our new Audi…RB
Hey I also noticed they put the drivers wheel on the wrong side also…Ha!…RB
Thank God that the consumers in America have the lemon law as a failsafe. I had my 2003 Mini Cooper bought back after over eight months of “working” with the company for a resolution. When I first saw the mechanics of the cabrio top, I knew there would be issues with it’s operation scattered throughout production. Even though it has received wide acclaim for its innovative design, issues were bound to pop up (or not “pop up”) once it was released. You have two entirely seperate systems opening this top. One mechanical system to pull the sunroof back and then a hydraulic system to fold the roof down. This doubles your chances for troubles. As long as everything works it’s a wonderful design. However, after seeing your brand new car spend 41 days in 11 months sitting in the shop for repairs, one tends to become a bit jaded.
I don’t know the letter of the law in the UK, and I haven’t read the whole sorry tale, but I would think that if the thing failed on delivery, he’s got a very good case. If it had been me, I think I might have refused delivery right there. Let the dealer use it as a demo (ha!) and wait for one that works.
Here is another broken convertible roof; don’t read about them much so the mechanism reliability must be reasonably good – still reading about worn cloth though.