The song does not say which George, but it does feature the Battle of Waterloo, during which George III was king. However, I agree that he does not deserve credit for Wellington's victory. In fact, in his later years he suffered from dementia. See the movie The Madness of King George. Henry V was actually present at Agincourt, but later monarchs get too much credit for their military forces' triumphs.
It was King George III and the House of Lords at that time, that are in that song/aria.
Oh I've seen THE MADNESS of KING GEORGE" several times and really like the movie. I also have a bio about King George III, as well as several books that are devoted to all of the Kings and Queens of Britain/the UK, as well as some others, each of which are about each of the ruling Houses, and those kings & queens, throughout time.
Yes, the earlier Kings ( though not John! )all went into battle themselves; Saxons ones, Norman ones, Plantagent, and Tudors too.