In this paper, I take Capital in the Twenty-First Century by Thomas Piketty as the starting point for a set of twelve policy proposals that could bring about a genuine shift in the distribution of income towards less inequality. In designing the set of proposals, I draw on the experience of reducing inequality in postwar Europe and on an analysis as to how the economic circumstances are now different in the twenty-first century, highlighting the role of technical change and the rise in capital emphasized by Piketty. The proposed measures span many fields of policy, and are not confined to fiscal redistribution, encompassing science policy, competition policy, public employment, a guaranteed return on small savings, a capital endowment, as well as more progressive taxation of income and wealth transfers, and a participation income. Inequality is embedded in our social structure, and the search for a significant reduction requires us to examine all aspects of our society. I focus on inequality within countries, and what can be achieved by national governments, with the UK specifically in mind. The primary audience is those concerned with policy-making in national governments, but implementation should not be seen purely in these terms. There are different levels of government, and certain proposals, particularly those concerned with taxation, may only be feasible if pursued by a group of countries in collaboration. The last of the twelve proposals - for a basic income for children - is specifically directed at the European Union. Finally, actions by individuals as consumers, as workers, or as employers, can all contribute to reducing inequality.