This paper explores the historical relationship between the expansion of the UK HE system through sectorial diversification, processes of differentiation/convergence and (in)equalities since the 1960s. It examines the extent to which the connections and tensions between three stories of resource, mission and social differentiations might be influenced (alongside other forces) by the emergence and crisis of successive socio-economic regimes. The empirical analysis of the three types of differentiation compares and contrasts new historical data on funding, enrolment and qualifications for the whole system and its institutional segments. The analysis shows that the ongoing tensions between resource, mission and social differentiations were exacerbated by the effect of the crises of 1973 and 2008 which provoked their misalignment and the destabilisation of the phases of expansion started in the 1960s and the 1990s. This pleads for a new social compromise to overcome the 2008 crisis to which a new HE expansion based on a realignment of, rather than a trade-off between the three dimensions of differentiation might contribute. This realignment requires a reversal of the public/private substitution of funding ensuring that a less unequal resource differentiation reflects and drives fairer processes of mission differentiation or convergence rather than stratifying social inequalities.