Getting the lid off a close-coupled toilet cistern. ?

I've got a close-coupled dual flush cistern which is developing flushing 'issues'. No brand name visible, but got it from B&Q a few years ago. My problem is getting the lid off the cistern to gain access to the working bits. It doesn't just lift off and you don't seem to be able to lift up or screw off the flush button mechanism. The outer ring of the flush buttons rests on the aperture in the ceramic lid, so you obviously have to get the mechanism off before you can release the lid... I don't want to force it, and though a keen DIYer and amateur plumber, this is baffling me. Any ideas?