I had to get the window motor replaced on my old mcs, can't remember how much it cost unfortunately. As far as I remember a good thump with your fist to the inside of the door sometimes gets it working again.
Had this on my 52 plate mini last year; just give the door a good thump a couple of times just above the speaker. Have to hit it pretty hard, but it does the trick!! Not had aproblem with mine ever since.