I have an 02 Mini One Auto which has just done over 63,000 miles. Last week the gearbox starting whining when in Drive as the gears change up and down. I have taken it to my local garage (non Mini) who have advised that the gearbox requires replacing at a cost of £2,600!!! The car has a full main dealer Mini Service history. I would expect a gearbox to last more than 63,000 miles on a 7 year old car.

Is anyone aware of a similar problem/cause and if so have Mini (BMW) acknowledged there is a problem?

If you search through the CVT forum you'll find a number of other CVT owners who have experienced problems. To the best of my knowledge MINI has never acknowledged that the CVT has a problem, but of course they replaced the CVT with an automatic transmission in later models. Personally, I'm not convinced the CVT is particularly trouble prone, but it is expensive to replace and replacement seems to be the only fix when a CVT goes bad.