To what extent and why do social origins matter for access to higher education, including access to elite universities? What is the role of private and selective schooling? This paper uses the 1970 British Cohort Study (BCS70) to analyse the trajectories of a generation currently in early middle age. We find that the influence of social origins, especially parental education, remains when both a wide range of cognitive measures and school attainment are controlled. Attending a private school is powerfully predictive of gaining a university degree, and especially a degree from an elite institution, while grammar schooling does not appear to confer any advantage.