(rather than cherry picking fees to say how much more UK universities could charge)
Comparing universities with similar QS rankings is a fair benchmark, given the previous comment about UK academics not being comparable to academics at top US academics.
There is no way that the average UK universities run as 'businesses' as user suggested could provide that level of financial aid. They would also have to transform themselves to provide the same sort of teaching package and facilities that these top private colleges provide.
But this is precisely the point - and relates to the strikes.
UK higher education is in an unstable equilibrium at the moment, poised midway between the business model in the US and the publicly funded models of Europe.
The management of the top UK universities wants to move further towards the US model: less money spent on academic staff, less staff on permanent contracts, more money spent on facilities to attract students, more money spent on packages to attract students (including possible fee subsidies). They want to be able to take out big bonds (look at what Oxford did...) to fund their plans, and they want to change the staff pensions to improve their bottom lines and get better rates for bonds. It is not an accident that Oxbridge colleges were one of the biggest supporters of lower risk for the USS pension fund.
Parents should be opposed to these changes, because if we move to the US system higher education is going to become more expensive and less accessible.
Right now, people complain that you don't get the same value for 9k from all universities. But you also don't have to pay 9k - you pay back according to your income, so if your degree doesn't lead to a well paid job you actually pay back much less. If we move further towards the US system, the very top UK universities will form a super league and charge much more (*). They would almost certainly have to introduce more "student aid", underwriting student loans for poorer students, but loans directly from universities would not be on the same terms as current student loans - they would have to be paid back in full, regardless of future income.
(*) It is pointless to fight about whether much more will be 12k, 15k or 20k and how much places like UCL, Warwick, Durham etc could get away with charging. The point is that it would be more, and that students would have to pay more back because it would be done via loans rather than graduate tax.