Thats a tricky one, as in my Audi A4 I had told my insurance I would do 10,000 a year (it was my first car and I genuinely had no idea what mileage I would do). Anyway, I wrote it off, having owned it for a year and having driven about 16,000 miles. They never asked any questions, and payed up no problems.
I was thinking though. Say you insured your car for a year, and after 4 months, you got your MOT done. And then for arguments sake you had an accident 9 months into the year. If you had driven more than the quoted total mileage in the time between the MOT (as the mileage is recorded on the MOT) and the accident, then the insurers would have documented evidence that you had done to many miles thus giving them the oportunity to void your insurance. Although I don't know if they would go into that much detail.
I have never been asked the current mileage of any of my cars when buying insurance, so I can't see how they could prove it otherwise, without maybe contacing BMW to find out about your mileage at service vists etc. Although I doubt this information would be disclosed anyway, as BMW are not likely to stitch up their own customers for fear of losing business.