The discussion of health inequalities in Britain (e.g. in the Black Report) has been conducted largely on the basis of social class mortality differentials measured by achieved social class and not by social class of origin. It is shown in this paper that social class mortality differentials by achieved social class are not invariant to the rate of social mobility and that the use of them is likely to result in a biased measure of trends in health inequalities when the absolute rate of social mobility varies over time. It is further shown that if, as is likely, health status is a factor systematically affecting the probability for an individual of upward or downward social mobility, then an increase in the rate of social mobility may well result in constant or widening social class mortality differentials by achieved social class even if the differentials are narrowing when measured by social class of origin. It is claimed that this process may well explain why the observed social class mortality differentials, which are measured by achieved social class, have not fallen in Britain during the post-1945 period.