Education--and in particular higher education--is often regarded as a route to social mobility. For this to be the case, however, the link between family background and adult outcomes must be broken (or at least reduced) once we take account of an individual's education history. This paper provides new evidence on differences in graduates' earnings by socio-economic background, exploiting rich individual-level data to account for more of the ways in which graduates from different socio-economic backgrounds differ from each other than has been possible in previous research on this topic. We continue to find significant differences between the earnings of graduates from lower and higher socio-economic backgrounds, even after accounting for a rich array of characteristics, skills and experiences from before individuals went to university, as well as their labour market experiences subsequently. These results suggest that it is not enough simply to encourage more young people to go to university, or even to ensure that they graduate with "good" degrees; policymakers interested in increasing social mobility also need to focus on what happens to them once they leave university to ensure that higher education is truly able to "level the playing field" between those from different socio-economic backgrounds.