Combating child poverty is desirable to ensure equality of opportunities across children, as well as fostering the sustainability of the societal well-being for future generations. This paper focuses on the study of child poverty in the 28 Member States of the European Union over the period 2008–2018. We analyse the relationship between child poverty and government social expenditure by controlling it with tax structure (ratio direct taxes over indirect taxes), economic growth and socio-demographic characteristics. For that, we rely on panel data methodology. This paper has verified that the effectiveness of the government social spending programmes to reduce child poverty also depends on the progressiveness of the country’s tax structure. Government spending on health and education programmes could be more effective in reducing child poverty in Member States with less progressive tax structure, provided they reached the average level of public spending for the whole of the European Union. By contrast, a positive relationship between child poverty and government social protection spending regardless of the tax structure of countries was found. In this case, the underlying forces that lead to less effectiveness of social protection programmes are also stronger in the less progressive Member States.