In recent years, healthcare has become a fundamental pillar of the level of well-being of any society. With the aim of improving the lives of countries and societies, in 2015 the United Nations (UN) approved the 2030 Agenda for Sustainable Development. Among the Sustainable Development Goals (SDGs) set out in the Agenda are health and well-being (O3) and the reduction of inequalities (O10). The general objective of this paper is to analyse the impact that the level of socioeconomic development, as well as the evolution of inequalities, have had on public spending on health in European Union countries. The research methodology is based on the application of a regression model and statistical techniques such as sigma convergence, beta convergence and the Gini index. We can see that the levels of public spending on health per capita, the level of socio-economic development and the degree of inequality are closely related in these countries. For this reason, we suggest maintaining sustainable economic growth to reduce the economic disparities between EU countries, and also the current differences in public spending on health per capita.