The objective is to describe age-specific cumulative incidence for hospital-recorded indicators of chronic health conditions (CHCs) in children with Down syndrome (DS) compared with children without DS. National birth cohort using hospital admission and death records. National Health Service (NHS)-funded hospitals in England. Liveborn, singleton infants born in NHS-funded hospitals between 2003 and 2019. Cumulative incidence of nine categories of hospital-recorded CHCs, multimorbidity and mortality. We identified 10 621 infants with DS among 9 631 646 liveborn, singleton infants (0.11%). Among children with DS, the cumulative incidence for any indicated CHC was 90.1% by age 16, as compared with 21.2% of children without DS. By age 16, a third of children (33.1%) with DS had CHCs affecting four or more body systems; only 6.0% of children without DS had CHCs indicated in more than one body system. The most common CHCs in children with DS were severe congenital heart defects, indicated in 57.2% (0.8% in children without DS). The estimated HR for mortality up to age 16 comparing children with versus without DS was 15.26 (95% CI: 14.15, 16.45). Children with DS had a higher cumulative incidence for CHCs in each body system category and subcategory, at all ages, than children without DS. Multimorbidity and mortality were higher among children with DS. Administrative data can be used to examine the health needs and healthcare use of children with DS throughout childhood and adolescence.