I'm afraid I had the same problem, and I know there are others. We're all victims to the Midlands gearbox which comes standard with most first generation Coopers (they were upgraded after 2004 I believe). When my Cooper was in gear it'd get a terribly loud whine, and the whine would rise/fall in pitch as you were accelerating/decelerating, respectively.
I believe you can eliminate the thrust bearing as that would be more likely to give noise during the motion of pushing the clutch in. The source of your problem is likely to be the bearings inside the gearbox. My money's on either the input shaft bearings or the differential bearings. Not wanting to pull my gearbox apart, I replaced my whole unit with a 6 speed gearbox from a Cooper S. Worth every dollar, but it's a bit of effort and requires other parts. I recommend having a mechanic listen to the noise and give you a solid second opinion on the noise before taking action - transmission work can be pricy.