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Taxing tobacco is one of the most effective ways to reduce smoking prevalence, mitigate its devastating consequential health harms and progress towards a tobacco-free society. This study modelled the health and economic impacts of increasing the existing cigarette tobacco duty escalator (TDE) in the UK from the current 2% above consumer price inflation to 5%.A two-stage modelling process was used. First, a non-linear multivariate regression model was fitted to cross-sectional smoking data, creating longitudinal projections from 2015 to 2035. Second, these projections were used to predict the future incidence, prevalence and cost of 17 smoking-related diseases using a Monte Carlo microsimulation approach. A sustained increase in the duty escalator was evaluated against a baseline of continuing historical smoking trends and the existing duty escalator.A sustained increase in the TDE is projected to reduce adult smoking prevalence to 6% in 2035, from 10% in a baseline scenario. After increasing the TDE, only 65% of female and 60% of male would-be smokers would actually be smoking in 2035. The intervention is projected to avoid around 75 200 new cases of smoking-related diseases between 2015 and 2035. In 2035 alone, £49 m in National Health Service and social care costs and £192 m in societal premature mortality and morbidity costs are projected to be avoided.Increasing the UK TDE to 5% above inflation could effectively reduce smoking prevalence, prevent diseases and avoid healthcare costs. It would deliver substantial progress towards a tobacco-free society and should be implemented by the UK Government with urgency.