I used a flat bladed screwdriver to pry out the head of the push rivet. You should then be able to pull the whole rivet out.
This is a basic industrial push rivet. Obviously the ones on the MINI are slightly larger but they work in the same way.
Chip used a special tool, which is a far more reliable method than the way I did it.
http://www.mini2.com/forum/2996508-post15.html