Introduction Older people have been reported to be at higher risk of COVID-19 mortality. This study explored the factors mediating this association and whether older age was associated with increased mortality risk in the absence of other risk factors. Methods In UK Biobank, a population cohort study, baseline data were linked to COVID-19 deaths. Poisson regression was used to study the association between current age and COVID-19 mortality. Results Among eligible participants, 438 (0.09%) died of COVID-19. Current age was associated exponentially with COVID-19 mortality. Overall, participants aged ≥75 years were at 13-fold (95% CI 9.13–17.85) mortality risk compared with those <65 years. Low forced expiratory volume in 1 second, high systolic blood pressure, low handgrip strength, and multiple long-term conditions were significant mediators, and collectively explained 39.3% of their excess risk. The associations between these risk factors and COVID-19 mortality were stronger among older participants. Participants aged ≥75 without additional risk factors were at 4-fold risk (95% CI 1.57–9.96, P = 0.004) compared with all participants aged <65 years. Conclusions Higher COVID-19 mortality among older adults was partially explained by other risk factors. ‘Healthy’ older adults were at much lower risk. Nonetheless, older age was an independent risk factor for COVID-19 mortality.