Edmund Conway is wrong about the causes of inequality being rich countries imposing free trade on developing nations and the reduction in taxation in the Reagan/Thatcher era in the UK and USA. Since 1980, Britain's tax burden has risen by over 2% and the tax burden in the US has risen more rapidly than that almost anywhere else in the developed world. In Sweden, on the other hand, the tax burden has fallen sharply and is set to fall further. Also, free trade has reduced absolute poverty enormously - especially across Asia. It is countries that have rejected free trade policies that remain desperately poor. Trade regulation concentrates power in the hands of elites in underdeveloped countries - it is a major cause of inequality and corruption.
Edmund Conway is right though that globalisation has helped to raise inequality by providing a greater range of entpreneurial opportunities, especially when combined with the revolution in technology. But we are all better off as a result. This process is helped by the increased mobility of labour which is at levels unseen since the First World War: there were few self-made Soviet millionaires living in Britain during the cold war - we can be thankful for these changes. Inequality will certainly not be eased by the current situation in the UK whereby any family with children earning below average earnings loses in taxes and "clawed back" tax credits 80% of every extra £1 they earn. If only Reagan and Thatcher had done what Edmund Conway suggests and really had reduced taxes.
See also the IEA monograph
Living with Leviathan: Public Spending, Taxes and Economic Performance  by David B. Smith.