Summary It has previously been shown that, across three British birth cohorts, relative rates of intergenerational social class mobility have remained at an essentially constant level among men and also among women who have worked only full time. We establish the pattern of this prevailing level of social fluidity and its sources and determine whether it also persists over time, and we bring out its implications for inequalities in relative mobility chances. We develop a parsimonious model for the log-odds-ratios which express the associations between individuals’ class origins and destinations. This model is derived from a topological model that comprises three kinds of readily interpretable binary characteristics and eight effects in all, each of which does, or does not, apply to particular cells of the mobility table, i.e. effects of class hierarchy, class inheritance and status affinity. Results show that the pattern as well as the level of social fluidity are essentially unchanged across the cohorts, that gender differences in this prevailing pattern are limited and that marked differences in the degree of inequality in relative mobility chances arise with long-range transitions where inheritance effects are reinforced by hierarchy effects that are not offset by status affinity effects.