The last monarch to actually take a day to day interest in the affairs of government, and actively work in a regular fashion politically beyond just the advice of ministers? George III, to be honest. He took an active role in the government, though one very much tempered by Parliament, and wielded his not insignificant influence to significant effect for much of the early part of his reign. What confuses it is that George III was an avowed believer in cooperation between the monarch and Parliament, and pretty much set the precedent for the monarch not interfering in politics; thus, after his initial missteps (which can largely be attributed to his youth), he generally would, publicly, support his government, though he did work actively behind the scenes to affect his government's policies.
The process of developing the modern monarchy started with William & Mary, whose accession had necessarily required Parliament's active support, and required the full support of a Cabinet from within the Privy Council, with the confidence of Parliament, to govern effectively. Under George I, the Cabinet acquired even more power, first, due to a certain level of disinterest on his part, and, second, after the South Sea bubble burst, when the first modern Prime Minister - the First Lord of the Treasury, Sir Robert Walpole - was effectively invested with the power and authority of both Crown and Parliament in response to the crisis.
George II and George III, unlike their predecessor, did actively and constantly intervene in political questions on a regular basis. The former had an unsteady relationship with Parliament, but, as I said above, George III moved his influence more into the background.
George IV, both as monarch and as Prince Regent, and later William IV, did intervene occasionally in government and political affairs, but not on any regular basis, while Victoria became influential due to the development of the United Kingdom's multi-party system, though she still acted on the advice of her ministers in almost all circumstances. George V's intervention in the Parliament Act 1911 was the last time the monarch directly intervened in the workings of Parliament, on behalf of the government, while Elizabeth II, as has already been said, has herself made a decision which was not clearly advised on in the normal fashion (though, even that was on the irregular advice of ministers).