At first I didn't think it could be that, because it wasn't constant, but then I noticed that I could pull the shift lever when it was already on its lowest gear and it would move further left before returning back to its position. Clearly when I shifted down, the derailleur moved to hit the spokes before springing back onto the largest sprocket. So turning the stop screw solved the issue.
I wish I hadn't decided to do the adjustment whilst I was halfway home though, because now my hands are absolutely freezing. Really appreciated the quick replies, considering my terrible choice of places to work on my bike.