As far as I can tell, it says to do all the things I've already tried. I've been through absolutely everything on this machine - hidden folders etc. - and downloaded both Disk Inventory and OmniSweeper to check it, but both apps can only see around 27GB on the HD, they can't see this other 31GB. There is still no way to find and delete this 'other'. I've also just managed to recover the computer after it crashed completely and wouldn't get past grey screen after login (safe booting just seemed to fix it....)
Still no idea what's going on. Oddly, there used to be another account on here called 'Guest' that I'm 99% sure had never been used (so I would expect there was nothing on there to account for all the 'other'), but since the crash the 'Guest' user has disappeared. How strange.
I'm going to get someone else to have a look at it physically and if neither of us can find anything I think I'm just going to have to try wiping it and starting over.
Thanks for your help!