The distribution of education by social background and the mobility prospects of society are intimately connected. To begin to predict future trends in mobility in the UK we bring together evidence on educational inequality by family background for cohorts from 1958 to 2000 for a range of educational outcomes. There is evidence that educational inequalities have narrowed among recent cohorts as the overall level of educational achievement has increased. This could be promising for mobility provided the labour market returns to these qualifications are maintained. However, stubborn inequalities by background at higher attainment levels imply that narrowing inequalities and expanding equality of opportunity throughout the educational distribution is a difficult task.