We will soon learn the answer in a few weeks. Lord Browne of Madingley (i.e., the former BP boss) is conducting a review of student fees at present. University fees (read "tuition fees" if North American) have a cap of about £3,200 for now. There are reports, such as from the BBC here, that fees may rise up to £7,000 or even £10,000 per year.
I believe it is a near certainty that tuition bills will rise, although it is difficult to predict how much. While I suspect £10,000 will not be the new cap in the end, I would be very surprised if something in the region of £5,000-7,000 was not proposed.
This is a further major change in higher education funding. Many of the parents of those beginning university now will have gone to university themselves for free....and many may have enjoyed free maintenance grants as well. This is all a very far cry from the support available for now.
Furthermore, higher fees seem almost inevitable when the current government is asking each department to cut its budget by 25% or more. It would seem that Michael Gove, the Education Minister, will have some of his work done for him by the Browne review and it's widely expected that the ability of universities to charge higher fees may be tied to some reduction in their teaching grants. We shall put a rest to such guesswork soon when the review is finally published.
Finally, it will be interesting to see how universities react. On the one hand, many will broadly welcome the opportunity to generate more income for further investment in their own institutions. On the other hand, there may be concerns that these higher fees come with many strings attached. For example, students paying higher fees may demand more services in return. This may make good sense if their higher fees actually did translate into higher revenue for universities. However, if these higher fees do no more than replace the investment that the government is withdrawing, then this will pose a challenge.