The discussion of social mobility tends to focus on the institutions that are dominated by the middle classes, which is all of them, so it is a very middle class conversation. It includes people from working class backgrounds, but only those who chose to be socially mobile, not the far greater number who did not.
These institutions are only relevant to the extent to which they interact with school children, which is not much, because the decision to relocate socially is not taken by adults, it is taken by kids. If you go back to when you were eleven or twelve, and picture yourself at home, can you imagine making a set of decisions that said to your family and friends 'I'm going to leave you behind in poverty and join a higher class of people as I, socially, rise above you'.
The problem is the idea that some people are better than others. Hand wringing prayers for more social mobility do not refute this idea, they cement it in place. Social mobility is an evil design; it is cruel to all the people who no one would ever describe as the 'lower orders', but if they did, we would know exactly who they meant. It is especially cruel to those who choose its 'upward' path, who must surrender their passports to their birth culture long before they are naturalised by their adopted one.
But in perfect step with Pandora's Box, as you would expect from a classically educated class, after the puke and the pestilence, there is hope. The lack of social mobility in our country disproves a Thatcherite notion that is hard wired into politics, that people's primary motivation is to maximise their own economic gain. The millions of people who choose not to succeed at school are choosing equality, placing their relationships with family and friends above personal gain.
It is an example we should all follow; inequality, after all, is nothing more than what we think of other people.