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Objectives: To model the impact on chronic disease of a tax on UK food and drink that internalises the wider costs to society of greenhouse gas (GHG) emissions and to estimate the potential revenue., Design: An econometric and comparative risk assessment modelling study., Setting: The UK., Participants: The UK adult population., Interventions: Two tax scenarios are modelled: (A) a tax of £2.72/tonne carbon dioxide equivalents (tCO2e)/100 g product applied to all food and drink groups with above average GHG emissions. (B) As with scenario (A) but food groups with emissions below average are subsidised to create a tax neutral scenario., Outcome Measures: Primary outcomes are change in UK population mortality from chronic diseases following the implementation of each taxation strategy, the change in the UK GHG emissions and the predicted revenue. Secondary outcomes are the changes to the micronutrient composition of the UK diet., Results: Scenario (A) results in 7770 (95% credible intervals 7150 to 8390) deaths averted and a reduction in GHG emissions of 18 683 (14 665to 22 889) ktCO2e/year. Estimated annual revenue is £2.02 (£1.98 to £2.06) billion. Scenario (B) results in 2685 (1966 to 3402) extra deaths and a reduction in GHG emissions of 15 228 (11 245to 19 492) ktCO2e/year., Conclusions: Incorporating the societal cost of GHG into the price of foods could save 7770 lives in the UK each year, reduce food-related GHG emissions and generate substantial tax revenue. The revenue neutral scenario (B) demonstrates that sustainability and health goals are not always aligned. Future work should focus on investigating the health impact by population subgroup and on designing fiscal strategies to promote both sustainable and healthy diets.