As in many other countries, government policy in the UK has the objective of raising the participation rate of young people in higher education, while increasing the share of the costs of higher education paid by students themselves. A rationale for the latter element comes from evidence of a high private return to university undergraduate degrees. However, much of this evidence pre-dates the rapid expansion in the graduate population. In the current paper, we use evidence from a cohort of young people born in Britain in 1970 to update influential evidence on returns to a first degree based on a previous 1958 birth cohort. We also analyse variations in returns by degree subject and by class of degree. Our analysis incorporates proxying and matching, control function and propensity score matching methods. Among other results, we find (i) that the returns to a first degree for men changed very little across the two cohorts while the return for women declined substantially and (ii) evidence of differences in returns to a first degree according to subject area of study and class of degree awarded.