BACKGROUND: In response to the COVID-19 pandemic, the UK first adopted physical distancing measures in March, 2020. Vaccines against SARS-CoV-2 became available in December, 2020. We explored the health and economic value of introducing SARS-CoV-2 immunisation alongside physical distancing in the UK to gain insights about possible future scenarios in a post-vaccination era. METHODS: We used an age-structured dynamic transmission and economic model to explore different scenarios of UK mass immunisation programmes over 10 years. We compared vaccinating 75% of individuals aged 15 years or older (and annually revaccinating 50% of individuals aged 15-64 years and 75% of individuals aged 65 years or older) to no vaccination. We assumed either 50% vaccine efficacy against disease and 45-week protection (worst-case scenario) or 95% vaccine efficacy against infection and 3-year protection (best-case scenario). Natural immunity was assumed to wane within 45 weeks. We also explored the additional impact of physical distancing on vaccination by assuming either an initial lockdown followed by voluntary physical distancing, or an initial lockdown followed by increased physical distancing mandated above a certain threshold of incident daily infections. We considered benefits in terms of quality-adjusted life-years (QALYs) and costs, both to the health-care payer and the national economy. We discounted future costs and QALYs at 3·5% annually and assumed a monetary value per QALY of £20 000 and a conservative long-run cost per vaccine dose of £15. We explored and varied these parameters in sensitivity analyses. We expressed the health and economic benefits of each scenario with the net monetary value: QALYs × (monetary value per QALY) - costs. FINDINGS: Without the initial lockdown, vaccination, and increased physical distancing, we estimated 148·0 million (95% uncertainty interval 48·5-198·8) COVID-19 cases and 3·1 million (0·84-4·5) deaths would occur in the UK over 10 years. In the best-case scenario, vaccination minimises community transmission without future periods of increased physical distancing, whereas SARS-CoV-2 becomes endemic with biannual epidemics in the worst-case scenario. Ongoing transmission is also expected in intermediate scenarios with vaccine efficacy similar to published clinical trial data. From a health-care perspective, introducing vaccination leads to incremental net monetary values ranging from £12·0 billion to £334·7 billion in the best-case scenario and from -£1·1 billion to £56·9 billion in the worst-case scenario. Incremental net monetary values of increased physical distancing might be negative from a societal perspective if national economy losses are persistent and large. INTERPRETATION: Our model findings highlight the substantial health and economic value of introducing SARS-CoV-2 vaccination. Smaller outbreaks could continue even with vaccines, but population-wide implementation of increased physical distancing might no longer be justifiable. Our study provides early insights about possible future post-vaccination scenarios from an economic and epidemiological perspective. FUNDING: National Institute for Health Research, European Commission, Bill & Melinda Gates Foundation.