I think it's fair to say that the DD who did an Oxford masters after an Oxford undergrad was probably in a stronger position to get full funding for a four year PhD, so there may well be some medium/long term financial advantage in the bigger names.
This is a bit of an over generalization.
Quite a few Oxbridge masters are cash cows for their departments. Of course a top student graduating from such a course will get good offers, but a medium student won't necessarily get better offers than they would have gotten after a masters from a place you don't call a "big name". This applies particularly for specialisms in which Oxbridge is top 5 or top 10 but not top 3.
It would have been better to make a loan available expressed as a percentage of the fees plus living costs at each institution I'd have thought.
But this would be utterly unfair, since Oxbridge and London courses are expensive but not better quality. 50% of the total costs at Bristol/Warwick/Exeter might be £8000 while 50% of the total costs in London might be £14k, with the London institution charging twice as much for a comparable course.
Why on earth should the student loan system subsidise London universities charging very high fees? Why should the loan system pay more for somebody studying at UCL if e.g. York had an equally or more respected programme in that specific subject? Since London and Oxbridge have so many international students who are paying even more, the onus is rather on them to use their international fees to make the costs more affordable for EU students.
Anyhow in reality if the system was a percentage of the fees then you can bet that universities would push up their fees to get the most out of the new system.