It's a bit of a judgement call of course, but I'd say the last monarch who exercised considerable political power was George V (reign 1910-1936) as he was essential in reducing the power of the House of Lords in 1911. The Liberal party had had a majority in Commons since 1905, but had a number of significant bills either rejected outright or hopelessly amended the Conservatives in the House of Lords. The most significant case was when in 1909 Lords vetoed a budget bill, which traditionally they didn't do even though they technically had the power. A modified version of the bill was passed after elections but the Commons vs. Lords thing had become a big issue. What became the Parliament Act of 1911 was proposed, and it reduced Lords to the powers to delay a bill and to do nothing about budgets. Since Lords still had veto power before the Parliament Act was passed, how could you get Lords to pass it? George V threatened to appoint enough Liberal peers to pass the bill if the existing Lords didn't. It passed without having to appoint any new peers. It's hard to imagine Lords voting to reduce their own power without the intervention of George V.