The recruitment of black and Asian migrant workers in the 1950s and 1960s to the least desirable sectors of the British labour market arguably ‐ for some commentators ‐ set in motion a cycle of cumulative disadvantage, with the disadvantage experienced by migrant workers inhibiting the opportunities of their sons and daughters. While some of the more recent commentators have concentrated on the persistence of disadvantage, others have begun to indicate the progress made by the minority ethnic groups relative to whites. This article evaluates the character of that progress for the period 1966–1991, through a secondary analysis of published data from the decennial census and the Labour Force Survey. Despite the disadvantaged start for the black and Asian minority ethnic groups, and despite the persistence of discrimination, they have made considerable progress over this time‐span relative to whites in terms of their membership of the Registrar General's socio‐economic groups. The decline in differentials has occurred in the context of upward collective social mobility for each of the three main minority ethnic groups during the period. However, substantial gender differences continue to characterize the labour market distribution of each of the groups and, on the whole, they are more substantial than ethnic group differences.