Fetal alcohol spectrum disorders (FASDs) are lifelong disabilities caused by prenatal alcohol exposure. Prenatal alcohol use is common in the UK, but FASD prevalence was unknown. Prevalence estimates are essential for informing FASD prevention, identification and support. We applied novel screening algorithms to existing data to estimate the screening prevalence of FASD. Data were from a population-based cohort study (ALSPAC), which recruited pregnant women with expected delivery dates between 1991 and 1992 from the Bristol area of the UK. We evaluated different missing data strategies by comparing results from complete case, single imputation (which assumed that missing data indicated no exposure and no impairment), and multiple imputation methods. 6.0% of children screened positive for FASD in the analysis that used the single imputation method (total N = 13,495), 7.2% in complete case analysis (total N = 223) and 17.0% in the analysis with multiply imputed data (total N = 13,495). A positive FASD screen was more common among children of lower socioeconomic status and children from unplanned pregnancies. Our analyses showed that the complete case and single imputation methods that are commonly used in FASD prevalence studies are likely to underestimate FASD prevalence. Although not equivalent to a formal diagnosis, these screening prevalence estimates suggest that FASD is likely to be a significant public health concern in the UK. Given current patterns of alcohol consumption and recent changes in prenatal guidance, active case ascertainment studies are urgently needed to further clarify the current epidemiology of FASD in the general population of the UK.