Toilet Cistern pushbutton removal?

How do I remove the push button (double) from the lid of my low level, close coupled toilet cistern? When I attempt to raise the lid, it will not move by more than a couple of millimetres. If I attempt to rotate the escutcheon around the pushbutton, it will turn (anticlockwise) by only about 30 degrees, then the whole unit begins to turn. If I attempt to prise it off vertically, there is a lot of resistance that makes me feel I will break it if I try harder. I have another toilet where I can raise the cistern lid as the flush mechanism is connected flexibly to the pushbutton, but not on this problem one.
Many thanks,