I always unplug my 360, don't trust it not to overheat
Anyway, my problem has been fixed! Firstly I took the original copy I had back to Game and swapped it. That didn't fix it on its own but I noticed at the point where it always locked up that the disc stopped spinning and the fan stopped whirring too. This didn't happen with the new disc but the console still locked up.
So, I deleted all my saves and started again and i've just got past the point where it failed last time! So for me it seemed to be a mixture of a dodgy disc and a corrupted save file.