I would think with an 11/61 plate MINI, the owners who havent had them long are still enjoying them and dont intend to get rid of them yet, thats why youre finding it difficult to locate a used one.
Anyone buying a new car last year then selling it this year isnt very good on their pocket money wise.
I think a MINI dealer would be the best bet actually, maybe a low mileage demo car or similar?
Or if youre not too bothered about the odd dent and scuff mark, how about an ex rental one? only driven up to 10,000 miles then got rid of?
Enquire at one of the car rental companies if they have any coming up for disposal, problem with that is they would have had 1000, maybe not so careful drivers.