Little is known about morbidity for children with rare structural congenital anomalies. This European, population-based data-linkage cohort study analysed data on hospitalisations and surgical procedures for 5948 children born 1995–2014 with 18 rare structural congenital anomalies from nine EUROCAT registries in five countries. In the first year of life, the median length of stay (LOS) ranged from 3.5 days (anotia) to 53.8 days (atresia of bile ducts). Generally, children with gastrointestinal anomalies, bladder anomalies and Prune-Belly had the longest LOS. At ages 1–4, the median LOS per year was ≤3 days for most anomalies. The proportion of children having surgery before age 5 years ranged from 40% to 100%. The median number of surgical procedures for those under 5 years was two or more for 14 of the 18 anomalies and the highest for children with Prune-Belly at 7.4 (95% CI 2.5–12.3). The median age at first surgery for children with atresia of bile ducts was 8.4 weeks (95% CI 7.6–9.2) which is older than international recommendations. Results from the subset of registries with data up to 10 years of age showed that the need for hospitalisations and surgery continued. The burden of disease in early childhood is high for children with rare structural congenital anomalies.