In my place the VC is openly lobbying for a rare card fees system. So history might be £12k per year, medicine would be £100k and for the institution to be able to charge more than lower ranked universities. There seems to be no recognition that this would mean only rich people get to go to uni, and only very very rich people would be able to do something like medicine from Oxbridge, presumably because to make it to being a VC you're probably from a pretty privileged background yourself and have no idea about how normal people live.
I can see how appealing it would be for universities to do so given financial strains. It would cause uproar for a while but our UK students now only make up 20% of our cohorts.