The UK government has expressed a desire to increase social mobility, with policies to help achieve this aim focused on reducing inequalities in educational attainment. This paper draws together established and new information about the contribution that higher education can make to social mobility using a life-course approach, considering differences by family background in terms of university attendance and achievement, as well as occupation and earnings following graduation. We find substantial socio-economic differences at each stage. Young people from poorer backgrounds are, on average, less likely to go to university than their richer peers. Even among the selected group who do go to university, they are less likely to attend the highest status institutions, less likely to graduate, and less likely to achieve the highest degree classes. These differences in degree outcomes contribute to the lower average earnings of graduates from poorer families, but earnings differentials go well beyond those driven purely by degree attainment or institution attended. The evidence strongly suggests that, even after taking these factors into account, graduates from affluent families are more likely to obtain a professional job and to see higher earnings growth in the labour market. We discuss the implications of these findings for the prospects of higher education as a route to greater social mobility.