Background UK legislatures are at different stages in the policy process for introducing a minimum price for alcohol. Although there is evidence about the effectiveness of such policies, political and public concern exists about the potential effects on low-income drinkers. We present appraisals of the effects of a £0·45 minimum unit price (MUP; 1 unit=8g/10mL ethanol) policy in England in 2014—15 across the income and socioeconomic distributions. Methods We undertook policy appraisals using the Sheffield Alcohol Policy Model (SAPM version 2.6), a causal, deterministic, epidemiological model. SAPM accounts for differential alcohol purchasing and consumption preferences for population subgroups defined, using self-reported survey data, by age, sex, consumption level, and income or socioeconomic group. We derived volumes purchased and prices paid for ten alcoholic beverage categories (beer, cider, wine, spirits, and ready-to-drink beverages [RTDs], purchased in the on trade [eg, bars] or off trade [eg, shops]) from household-level 2-week spending diaries. A 10 × 10 price elasticity matrix was estimated to describe the relation between price changes and purchasing changes (assumed to represent consumption changes). After a policy change, the elasticity matrix was used to adjust individual-level survey data on self-reported mean weekly and peak daily alcohol consumption. We modelled resulting effects on mortality and disease prevalence using functions relating consumption measures to risk of having 47 chronic or acute disorders wholly or partly attributable to alcohol. Baseline mortality and morbidity rates were those reported for England and Wales in 2005 by the North West Public Health Observatory. These rates are adjusted to account for socioeconomic variability in mortality and morbidity risk with Office for National Statistics socioeconomic group-specific alcohol-related mortality data for 2001—03. Findings On average, moderate drinkers purchase 36 below-MUP units per year whereas harmful drinkers in the lowest and highest income groups purchase 1610 and 712 units, respectively. The policy is estimated to have small effects on moderate drinkers' alcohol consumption (—1·6 units per drinker per year) and spending (£0·78 per year). Bigger behavioural changes are estimated to occur among harmful drinkers and these are largest in the lowest income quintile (—300 units, —£34·63) compared with the highest (—34 units, £16·35). The same pattern of results was noted in sensitivity analyses using (a) alternative elasticity matrices, and (b) population subgroups defined by socioeconomic status rather than income. A list of published sensitivity analyses undertaken with SAPM is provided in the appendix. Health benefits from the policy are also unequally distributed due to differential baseline harm risks and purchasing patterns. Lower socioeconomic groups that make up 41·7% of the population would accrue 81·8% of the reduction in deaths and 87·1% of the reduction in quality-adjusted life-years lost. Interpretation Moderate drinkers, regardless of income, are only marginally affected by the policy because it chiefly targets harmful drinkers. Because they purchase more below-MUP alcohol, low-income harmful drinkers would be affected more than those with higher incomes. Policymakers must balance low-income harmful drinkers' larger consumption reductions against their greater health gains from reduced alcohol-related morbidity and mortality. Limitations of the model include supply-side responses not being considered (eg, retailers increasing prices above the MUP threshold) and the data used for adjusting baseline health risks for socioeconomic groups only relating to mortality and not being condition specific.