when Young wrote in 1958, only 5% of children went on to graduate from uni; since then, the landscape has changed (expansion of higher ed)
you don't need a uni degree to enter the elite but it certainly helps
50% of elites have a degree, though that rises to ~2/3 among the younger generation (25-50) so there's a generational factor too
the elite class has highest percentage of uni grads, though only 15% of the total pop of uni grads (established middle class has half; precariat has very few)
inequalities between unis: huge difference in elite/middle class ratios for top unis (oxbridge, University of London etc)
interesting spousal dynamics: marrying someone you met at uni -> household income advantage gets doubled (thus exacerbating household income inequality)
conclusion: simply expanding access to uni degrees won't unsettle social hierarchies, given the stratification among unis (that has developed due, at least partly, to expanded access imo)
Savage, M. (2015). A Tale of Two Campuses. In Savage, M. Social Class in the 21st Century. Pelican, pp. 219-258