The major impact of increasing tuition fees, is that tuition fee loans will increase. Pretty much nobody pays their fees themselves apart from International students. As has been said above, Student Finance is already pretty much at the tipping point of non-repayment. Increasing fees would only make that worse.
I suspect we're looking at a combination of fee increases, plus less favourable repayment terms e.g. lower earnings threshold to trigger repayments, higher interest rates, and no automatic cancellation if it isn't repaid by a certain point. My feeling is that student finance debt could potentially be something that you end up saddled with for your entire life.
In addition, social policy over the past few years has been to use uni as a holding pen for the 18-21 year olds, for whom there was insufficient paid work. The aim was to get as many school leavers into uni as possible. With the school leaving age now raised to 18 for everyone, I think the focus will change to getting more people into vocational training. Uni will again become something for a minority of people, sharply dropping the overall levels of student lending and debt.