National (and global) vaccination provides an opportunity to control the COVID-19 pandemic, which disease suppression by societal lockdown and individual behavioural changes will not. We modelled how vaccination through the UK's vaccine priority groups impacts deaths, hospital and ICU admissions from COVID-19. We used the UK COVID-19 vaccines delivery plan and publicly available data to estimate UK population by age group and vaccination priority group, including frontline health and social care workers and individuals deemed 'extreme clinical vulnerable' or 'high risk'. Using published data on numbers and distributions of COVID-19-related hospital and ICU admissions and deaths, we modelled the impact of vaccination by age group. We then modified the model to account for hospital and ICU admission, and death among health and social care workers and the population with extreme clinical vulnerability and high risk. Our model closely matches the government's estimates for mortality after vaccination of priority groups 1-4 and groups 1-9. The model shows vaccination will have a much slower impact on hospital and ICU admissions than on deaths. The early prioritisation of healthcare staff and clinically vulnerable patients increases the impact of vaccination on admissions and also protects the healthcare service. An inflection point, when 50% of the adult population has been vaccinated - with deaths reduced by 95% and hospital admissions by 80% - may be a useful point for re-evaluating vaccine prioritisation. Our model suggests substantial reductions in hospital and ICU admissions will not occur until late March and into April 2021.