In Britain and elsewhere, the influence of family socioeconomic status (SES) on education is already evident in primary school, and it persists and increases throughout the school years, with children from impoverished families earning lower grades and obtaining fewer educational qualifications than children from more privileged backgrounds. Reducing the effect of family background on children's education is a pivotal aim of educators, policymakers, and researchers, but the success of their efforts is poorly evidenced to date. Here, we show for the first time that over 95 years in Britain the association between family SES and children's primary school performance has remained stable. Across 16 British population cohorts born between 1921 and 2011 (N = 91,935), we confirmed previous findings of a correlation between family SES and children's school performance of 0.28 [95% Confidence Interval 0.22-0.34], after adjusting for cohort-specific confounders. Contrary to the popular assumption that family background inequality has increased over time, we observed only minimal differences in the association between family SES and school performance across British cohorts. We argue that education policies must prioritize equity in learning outcomes over equality in learning opportunities, if they seek to disrupt the perpetuation of social and economic inequality across generations. We speculate that the influence of family SES on children's education will only noticeably weaken if primary education settings become better equipped to meet and remediate the children's differential learning needs.