I was introduced to the King William quiz by a friend the other day. I don't know how I managed to miss finding out about it, as I used to read The Guardian, and it has been published in it since 1951 apparently. So I had a look at some of the previous years' quizzes. It helps (but not that much) if you know that each section has a theme.
Without googling or looking in books:
2005 quiz - I got 10 correct
2004 quiz - I got 8 correct
2003 quiz - I got 21 correct
I could have got a few (a very few) more if I had looked things up in books, for the ones where I knew what he was referring to, like poems, or food, or novels. For example, I knew that one question was three of the four subtitles of TS Eliot's Four Quartets, but couldn't remember for the life of me what the other one was.