I have just been searching for the answer to this very question, and wanted to post it here for others who are in this situation.
The answer is: if it is a dual-flush system (so there's a large button and a small button), you push the large button down, and while it's down use a flat head screw driver to pop the small button out, then do the same for the large button (using the space where the small button was to lever the big button out) and then you use the screw driver to unscrew the screw at the bottom holding the ring in place and then you can remove the cistern
Chris
April 2011