Abstract The implementation of determined or ambitious environmental policies may lead to regressive distributional impacts, disproportionately affecting low income population groups. The imposition of additional taxes on energy products affects negatively low-income households that face funding scarcity, increasing the risk of energy poverty. In this study, the state-of-the-art general equilibrium model GEM-E3-FIT is significantly expanded to represent ten income classes in all EU Member States. Each income class is differentiated by income sources, savings, and consumption patterns. We use the new modelling capabilities of GEM-E3-FIT to quantify the distributional impacts of European Union's ambitious emission reduction targets, in particular exploring their effects on income by skill and on energy-related expenditure by income class. The analysis shows that the transition to climate neutrality may increase modestly inequality across income classes, with low-income households facing the most negative effects. However, using carbon tax revenues as lump-sum transfers to support household income and as reduced social security contributions will increase employment and reduce income inequality across households in EU countries.