I find it interesting that someone described a 'glut' in recent graduates as being a reason for a diminished importance in the Oxford degree. I agree with the descriptive, but not the prescriptive part of that argument.
It is true that there are more degrees being awarded, but this is due largely to a far lower cutting-off point for A-level grades when it comes to continuing onto university. There are more uni students, but the numbers are swelling at the lower end of the grade scale, not the upper end. I think you must also recognise the factor of more easily achievable A grades at A-level (a tired point at this stage I know, but rather a realistic one).
So for many jobs you will have a few more degree-level candidates yes, but employers will find that many of these are of a lower calibre than they're used to when it comes to graduates. This, imo, will make them far more sensitive to the quality and background of a person's degree, and also probably its classification. Oxbridge will continue to be an instant and fairly reliable indication of quality, but that was always the case. The new development I think will be that employers start to make much finer distinctions between other universities. For example, employers might start to notice the difference between York and Essex, when before they were considered one and the same - these are both strong universities, but there will be less employers who afford them equal credit.
Quite separate from this, I think you *do* have an ongoing trend now of the top-tier uni's other than Oxbridge being given far more recognition as producing outstanding employees. This has been deserved for a very long time I think, for the likes of LSE, Imperial, Warwick or whatever, there is now far broader acceptance of their ability to often produce graduates of equal or higher quality than your average Oxbridge student.