Does that answer your question?
I know it's a bit of a pain having to register to get free, limited access to the FT but it is well worth it.
If you do you'll see that Gove was saying that past failings in the state sector are what has led to the continued dominance of private education in the higher reaches of parliament and the civil service. There's very little difference between the present cabinet and that of Robert Arthur Talbot Gascoyne-Cecil in 1902.
In other words, the entire history of the Labour party marks a failure to change the education system to increase opportunities for all.