They publish these same sort of stats about every three months. Here's the last one: www.hefce.ac.uk/media/hefce/content/pubs/2014/201403/HEFCE2014_03.pdf
The reporting is typically rather disingenuous.
Firstly, unis already do take school background into account, as is well publicised (and it's not merely a case of state vs private or comp vs grammar, there are things like which income quintile the school's catchment falls into).
The fact is that you can get into a university with any grades. So we are really talking about Oxbridge and the like here.
This article is 2 years old and explains quite clearly about how they do this already
www.theguardian.com/education/2012/jan/10/how-cambridge-admissions-really-work
It's certainly true that BBB from Shittown Comp is a better predictor of success than BBB from Eton, but the fact is that independent pupils enter with substantially better A Level grades (average ABB, versus BBC from state), and they leave with better degrees.
So there really isn't much point in talking about changing admissions, when this is already well-known.
And by the way, the difference is not that huge, for those with all As at A Level, there's no difference at all between state and private, below that you are talking about a BBB from a state school being as good (in terms of the number getting good degrees) as ABB from private. Hardly earth-shattering stuff - we are not taking students in with two Es from the ghetto and having them beat AAA students from Harrow. It's 1/3 to 1/2 of a grade higher, per A Level (depending on the level at which you are comparing), which rather puts paid to some of the nonsense about independent school students being spoonfed + clueless in comparison to their resourceful state-educated counterparts. Yes, BBB at state is better than BBB at private, but it's not as good as AAB, or AAA from a private school.