BACKGROUND: The role of children and staff in SARS-CoV-2 transmission outside and within households is still not fully understood when large numbers are in regular, frequent contact in schools. METHODS: We used the self-controlled case-series method during the alpha- and delta-dominant periods to explore the incidence of infection in periods around a household member infection, relative to periods without household infection, in a cohort of primary and secondary English schoolchildren and staff from November 2020 to July 2021. RESULTS: We found the relative incidence of infection in students and staff was highest in the 1-7 days following household infection, remaining high up to 14 days after, with risk also elevated in the 6--12 days before household infection. Younger students had a higher relative incidence following household infection, suggesting household transmission may play a more prominent role compared with older students. The relative incidence was also higher among students in the alpha variant dominant period. CONCLUSIONS: This analysis suggests SARS-CoV2 infection in children, young people and staff at English schools were more likely to be associated with within-household transmission than from outside the household, but that a small increased risk of seeding from outside is observed.