After finding that the wheel worked fine on wotty's ps4, I did a firmware update on the PC, a database rebuild on the PS4 in safe mode, then deleted and reinstalled the game. Still didn't work. Tried Driveclub....worked fine.
Then I noticed that deleting and reinstalling the game and all of it's updates, had still left the online storage settings intact. So I deleted them and hey presto, fixed. Lost all of my career progress but at least the wheel isn't faulty!
I will report it to Slightly Mad Studios in case anybody else gets the same corruption issues, but the vid below shows what was actually happening. Please don't mistake it for Timey's driving. It's very similar...
http://youtu.be/sQAiz7VIlxI