The Oxbridge thing is a convenient red herring squirrel, but I suspect it will run and run 
The real "meat" of the thread (IMO) is whether the VAT policy is of ultimate benefit to everybody. Which means discussion of what 'benefit' means and how one would measure it.
I notice that few supporters of the VAT policy are still pretending that 'benefit' means £££ VAT moolah bonanza for 6500 new teachers, a pile of Weetabix and some roof repairs. (Although in my experience once you have wetted Weetabix, it can set like concrete so maybe we could channel the Weetabix towards the building works.) Recent figures for movement of pupils from private to state, being at least 4-fold greater than the government's optimistic wild guess, would suggest that we'd best not define 'benefit' as a net gain for the taxpayer as it is looking likely the VAT policy will cost the government quite a lot of money.
The 'benefit' then could be improvements to educational attainment such as in advanced maths, language or science programmes. But the government have axed many of these in the past few months, to no complaint from policy supporters. On a previous thread, I recall a VAT supporter issued the eloquent response of "YAWN." And equally there is terrible provision for pupils needing special educational support, the powers that be seeming content to throw many SEN children to the wolves in order to keep costs down. So that doesn't seem to be it.
It looks to me that most likely remaining 'benefit' would be removal of educational choice so that all children are theoretically compelled to be educated together, leading to a utopian uniform melting pot of all abilities and social backgrounds. Since there is a massive diversity of state provision from better-than-private to absolutely disastrous, often associated with exactly the same parental financial resources that are so problematic if they're spent on private fees but not on house catchments or tuition, it's not clear how this utopianly uniform choiceless educational pot is going to be enforced.
Have I missed any 'benefits'?