A growing number of studies indicate a widening of socioeconomic inequalities in mortality over the past decades. It has therefore become crucially important to understand the impact of heterogeneity and its evolution on the future mortality of heterogeneous populations. In particular, recent developments in multi-population mortality have raised a number of questions, among which is the issue of evaluating cause-of-death reduction targets set by national and international institutions in the presence of heterogeneity. The aim of this paper is to show how the study of the population data and the population dynamics framework contribute to addressing these issues, by providing a new viewpoint on the evolution of aggregate mortality indicators in the presence of heterogeneity. Our findings rely on two datasets on the English population and cause-specific number of deaths by socioeconomic circumstances, over the period 1981-2015. The analysis of the data first highlights the complexity of recent demographic developments, characterized by significant composition changes in the population, with considerable variations according to the age class or cohort, along with a widening of socioeconomic inequalities. We then introduce a dynamic framework for studying the impact of composition changes on the mortality of the global population. In particular, we are interested in quantifying the impacts of cause-of-death mortality reduction in comparison with changes of composition in a heterogeneous population. We show how a cause of death reduction could be compensated for in the presence of heterogeneity, which could lead to misinterpretations when assessing public policies impacts and/or for the forecasting of future trends.