I find it interesting that nowhere in this thread has the difference between education and qualifications been raised.
When talking about the potential causal/correlative factors such as maternal education, and family income/wealth (also two very different things....high income doesn't necessarily mean high wealth IYSWIM), it's clear that these factors may just be proxies for some other kind of more or less amorphous influences (for example, no-one's mentioned class which is also interesting - traditional class analysis took the culture of different classes to be very different in respect to education - the middle classes typically valuing formal education, and particularly qualifications, in a way that wasn't quite the same in either the working or upper classes). And no-one's mentioned the difference that has occurred over the last 60 years with first the rise then the fall of the big postwar expansion of the grammar school and free university system, which created a very different climate for educational prospects for non-wealthy children in, say, 1965 compared to today. It's not surprising that if maternal education was once the biggest factor (acting as a proxy perhaps for the intersection of class, natural aptitude and culture), that in today's neoliberal capitalism pure wealth might have become the biggest factor, not necessarily because you can buy education or academic attainment, but because it can buy you the things that academic attainment used to be one way of helping you buy.
And qualifications are themselves a proxy for what we assume education to be - if you get a job at a management consultancy because you got a physics degree from Oxford you are probably not going to be asked technical solutions to mechanics problems in the interview. The piece of paper acts as a credential, but how much education stands behind it is not always clear, nor how it should guarantee that you should have a lucrative job. For those kinds of jobs the qualification just really serves as a way of credentialling yourself as a member of an elite - if you want a city job they are got by doing a lot of other things as well, mostly things that involve you having done other kinds of positional advantage that normally only wealth or class position can buy. It might look like you got that job because you have a degree from Oxbridge, but actually you got it because you did other things like look the right part, talk to the interviewers in ways they expected to be talked to, know people who could give you useful info about how to go about getting the job, have done informal work experience in the right places, and so on.