The high efficacy, low cost, and long shelf-life of the ChAdOx1 nCoV-19 vaccine positions it well for use in in diverse socioeconomic settings. Using data from clinical trials, an individual-based model was constructed to predict its 6-month population-level impact. Probabilistic sensitivity analyses evaluated the importance of epidemiological, demographic and logistical factors on vaccine effectiveness. Rollout at various levels of availability and delivery speed, conditional on vaccine efficacy profiles (efficacy of each dose and interval between doses) were explored in representative countries. We highlight how expedient vaccine delivery to high-risk groups is critical in mitigating COVID-19 disease and mortality. In scenarios where the availability of vaccine is insufficient for high-risk groups to receive two doses, administration of a single dose of is optimal, even when vaccine efficacy after one dose is just 75% of the two doses. These findings can help inform allocation strategies particularly in areas constrained by availability.