Background: Anthropogenic aerosols are a critical contributor to climate change and their net cooling effects can partially counter the warming effects of greenhouse gases, but they are rarely considered in health impact attribution studies of climate change. The aim of this study was to attribute heat-related deaths in Great Britain to anthropogenic climate change and individual forcings of greenhouse gases and aerosols. Methods: Using a special suite of climate simulations, past and future heat-related deaths in Great Britain attributable to the relative contributions of anthropogenic greenhouse gas and aerosol forcings were estimated under the Shared Socioeconomic Pathway SSP2-4.5. Empirical confidence intervals were quantified combining uncertainties from climate models and health risk functions. Findings: Emergence of heat-related mortality associated with anthropogenic climate change was partially counteracted by the cooling effects of aerosols, with the time of emergence being approximately four decades later compared with the greenhouse gas-only simulation. We estimate that around 700 annual heat-related deaths during 1961–1980 were masked by the cooling effects of aerosols. There was a sharp increase in heat-deaths between 1980 and 2020 due to the combined effects of greenhouse gas increases and large aerosol reductions. By the end of the 21st century, a 2–6-fold increase in heat-related deaths due to greenhouse gases is projected, with a negligible counteracting contribution of aerosols. Interpretation: In addition to greenhouse gases, the potential contributions of aerosols should be considered when assessing climate change risks and mitigation pathways. This is crucial due to their opposing temperature effects, diverging future emission trajectories, and varying geographical scales. Separate attribution of climate change impacts to the global effects of greenhouse gases and local effects of aerosols can enhance transparency and equity, and can inform loss and damage funding models. Such impact attribution assessments can help to optimise health co-benefits and prevent unintended negative consequences of environmental policies on heat-related and air pollution-related health outcomes. Funding: Health Protection Research Unit in Environmental Change and Health, National Institute for Health and Care Research.