Sorted!
Thanks for the advice alism – I deactivated all my plugins, and lo and behold, I could access my Permalinks config screen again. So I reset the permalinks to default and my site was up and running again. I’ve since reactivated all the plugins again and all seems fine.
Unfortunately, I didn’t take the scientific approach and deactivate the plugins one by one, so I don’t know which one was causing the conflict.
Does make me wary of using Permalinks again though…..
Thanks also to esmi for your initial suggestion.
Thanks guys!