I'm also studying at the Uni of Sheffield so hi there! I know i'm speaking from a slightly different point of view but if I had to pay a higher fee I certainly wouldn't be happy. A higher amount means more interest, which means higher debt and although true that most people do not end up paying off the whole amount, you've still got more to pay off. Say with £9000 fees at the moment, you may end up in £45,000 worth of debt. Well if you're lucky enough to be able to pay it all off, everything is all good. However if the same person had higher fees and a higher debt, they may be able to pay off the £45,000 but then they'll still be in debt due to the higher fees.
The fees are already extortionate and definitely don't need an increase. If I was in the position of applying to uni with fees higher than £9000, I'd probably think about other options.