We analysed the association of independent variables with non-verbal cognition at 6 years in children with complete data (3441 from a cohort of 9901), of whom 415 were anaesthetised before the age of 5 years. Using multivariable regression, cognition was reduced by a mean (95% CI) score for children: anaesthetised before the age of 5 years, 2.1 (0.7–3.5), p = 0.004; born prematurely, 9.8 (4.1–15.4), p = 0.001; whose mothers smoked while pregnant, 2.3 (0.8–3.8), p = 0.004; whose mothers had lower IQ scores, 0.3 (0.2–0.3) for each unit reduction in maternal IQ, p < 0.0001. The association of child IQ with exposure to anaesthetic drugs was sensitive to missing data.