In late 2020, the JCVI (the Joint Committee on Vaccination and Immunisation, which provides advice to the Department of Health and Social Care, England) made two important recommendations for the initial roll-out of the COVID-19 vaccine. The first was that vaccines should be targeted to older and vulnerable people, with the aim of maximally preventing disease rather than infection. The second was to increase the interval between first and second doses from 3 to 12 weeks. Here, we re-examine these recommendations through a mathematical model of SARS-CoV-2 infection in England. We show that targeting the most vulnerable had the biggest immediate impact (compared to targeting younger individuals who may be more responsible for transmission). The 12-week delay was also highly beneficial, estimated to have averted between 32-72 thousand hospital admissions and 4-9 thousand deaths over the first ten months of the campaign (December 2020–September 2021) depending on the assumed interaction between dose interval and efficacy.