It'll take an hour to download, so if anybody has any bright ideas in the next hour or so do let me know!
Edit: Done a bit of investigating: the capacity says 12.07 on iTunes (12.1 on the phone) but the coloured percentage meter thing on the bottom adds up to 14.1GB even though the figure on the left of that is 12.07GB. The 'free' is supposedly 2.2GB but it a tiny sliver (it says on the phone that 411MB is free), so I tried to sync a TV program (~800MB) and it wouldn't sync claiming the phone was full. Odd.