Background: Several countries are considering a minimum price policy for alcohol, but concerns exist about the potential effects on drinkers with low incomes. We aimed to assess the effect of a ??0??45 minimum unit price (1 unit is 8 g/10 mL ethanol) in England across the income and socioeconomic distributions. Methods: We used the Sheffield Alcohol Policy Model (SAPM) version 2.6, a causal, deterministic, epidemiological model, to assess effects of a minimum unit price policy. SAPM accounts for alcohol purchasing and consumption preferences for population subgroups including income and socioeconomic groups. Purchasing preferences are regarded as the types and volumes of alcohol beverages, prices paid, and the balance between on-trade (eg, bars) and off-trade (eg, shops). We estimated price elasticities from 9 years of survey data and did sensitivity analyses with alternative elasticities. We assessed effects of the policy on moderate, hazardous, and harmful drinkers, split into three socioeconomic groups (living in routine or manual households, intermediate households, and managerial or professional households). We examined policy effects on alcohol consumption, spending, rates of alcohol-related health harm, and opportunity costs associated with that harm. Rates of harm and costs were estimated for a 10 year period after policy implementation. We adjusted baseline rates of mortality and morbidity to account for differential risk between socioeconomic groups. Findings: Overall, a minimum unit price of ??0??45 led to an immediate reduction in consumption of 1??6% (-11??7 units per drinker per year) in our model. Moderate drinkers were least affected in terms of consumption (-3??8 units per drinker per year for the lowest income quintile vs 0??8 units increase for the highest income quintile) and spending (increase in spending of ??0??04 vs ??1??86 per year). The greatest behavioural changes occurred in harmful drinkers (change in consumption of -3??7% or -138??2 units per drinker per year, with a decrease in spending of ??4??01), especially in the lowest income quintile (-7??6% or -299??8 units per drinker per year, with a decrease in spending of ??34??63) compared with the highest income quintile (-1??0% or -34??3 units, with an increase in spending of ??16??35). Estimated health benefits from the policy were also unequally distributed. Individuals in the lowest socioeconomic group (living in routine or manual worker households and comprising 41??7% of the sample population) would accrue 81??8% of reductions in premature deaths and 87??1% of gains in terms of quality-adjusted life-years. Interpretation: Irrespective of income, moderate drinkers were little affected by a minimum unit price of ??0??45 in our model, with the greatest effects noted for harmful drinkers. Because harmful drinkers on low incomes purchase more alcohol at less than the minimum unit price threshold compared with other groups, they would be affected most by this policy. Large reductions in consumption in this group would however coincide with substantial health gains in terms of morbidity and mortality related to reduced alcohol consumption. ?? Holmes et al. Open Access article distributed under the terms of CC BY.