We analyse levels and trends of intergenerational social class mobility among three postwar birth cohorts in Britain and examine how much of the observed mobility or immobility in them could be accounted for by existing differences in educational attainment between people from different class backgrounds. We propose for this purpose a method which quantifies associations between categorical variables when we compare groups which differ only in the distribution of a mediating variable, such as education. This is analogous to estimation of indirect effects in causal mediation analysis but is here developed to define and estimate population associations of variables. We propose estimators for these associations which depend only on fitted values from models for the mediator and outcome variables, and propose variance estimators for them. The analysis shows that the part that differences in education play in intergenerational class mobility is by no means so dominant as has been supposed and that, while it varies with gender and with particular mobility transitions, it shows no tendency to change over time.