GordonD has the right idea. I used to work in a tire shop and we would leave one lug nut on and loose so the wheel wouldn't fall completely off, then would tap it loose from the other side.
Note that part of the MINI's maintenance schedule (it's in the owner's manual) is to grease the hubs so the wheels don't corrode to the hubs, which has happened in your case.
My S has some factory-applied grease right around the center of the hub and the wheels don't stick. If your grease is gone, time to reapply