I haven't rooted it yet, but I am definitely using the most recent Vodafone firmware update listed in this topic.
I only got my S4 recently, but my previous phone was rooted so I could use root level apps. I'd like to put my paid for Titanium Backup app to good use again, obviously it won't work till I root my S4. I do not want to remove TouchWiz, as surprisingly, I quite like the Stock rom compared to my old HTC which had to have itself purged of the evil that is HTC Sense LOL.
I tried the Motochopper exploit, no luck there.
I'm guessing from your reply CF-Root might be the way.