Climate change is expected to lead to changes in seasonal temperature-related mortality. However, this impact on health risk does not necessarily scale linearly with increasing temperature. By examining changes in risk relative to degrees of global warming, we show that there is a delayed emergence of the increase in summer mean mortality risk in England and Wales. Due to the relatively mild summer mean temperatures under the current climate and the non-linearity of the exposure–response relationships, minimal changes in summer mean risk are expected at lower levels of warming and an escalation in risk is projected beyond 2.5 °C of global warming relative to pre-industrial levels. In contrast, a 42% increase in mortality risk during summer heat extremes is already expected by 2 °C global warming. Winter attributable mortalities, on the other hand, are projected to decrease largely linearly with global warming in England and Wales.