Objective To estimate risks of major congenital anomaly (MCA) among children of mothers prescribed antidepressants during early pregnancy or diagnosed with depression but without antidepressant prescriptions. Design Population‐based cohort study. Setting Linked UK maternal–child primary care records. Population A total of 349 127 singletons liveborn between 1990 and 2009. Methods Odds ratios adjusted for maternal sociodemographics and comorbidities (aORs) were calculated for MCAs, comparing women with first‐trimester selective serotonin reuptake inhibitors (SSRIs) or tricyclic antidepressants (TCAs) and women with diagnosed but unmedicated depression, or women without diagnosed depression. Main outcome measures Fourteen system‐specific MCA groups classified according to the European Surveillance of Congenital Anomalies and five specific heart anomaly groups. Results Absolute risks of MCA were 2.7% (95% confidence interval, 95% CI, 2.6–2.8%) in children of mothers without diagnosed depression, 2.8% (95% CI 2.5–3.2%) in children of mothers with unmedicated depression, and 2.7% (95% CI 2.2–3.2%) and 3.1% (95% CI 2.2–4.1%) in children of mothers with SSRIs or TCAs, respectively. Compared with women without depression, MCA overall was not associated with unmedicated depression (aOR 1.07, 95% CI 0.96–1.18), SSRIs (aOR 1.01, 95% CI 0.88–1.17), or TCAs (aOR 1.09, 95% CI 0.87–1.38). Paroxetine was associated with increased heart anomalies (absolute risk 1.4% in the exposed group compared with 0.8% in women without depression; aOR 1.78, 95% CI 1.09–2.88), which decreased marginally when compared with women with diagnosed but unmedicated depression (aOR 1.67, 95% CI 1.00–2.80). Conclusions Overall MCA risk did not increase with maternal depression or with antidepressant prescriptions. Paroxetine was associated with increases of heart anomalies, although this could represent a chance finding from a large number of comparisons undertaken.