From Waterloo station (we used this station a lot on this trip and I couldn't get freakin' Abba out of my head for weeks.) it took about 40 minutes on a commuter train, then a 5 minute walk from the station to the palace. I loved it most of all because of the huge Kitchen tour. Gotta love the audio tour!
This clock reminded me of a clock I saw in a room in the Doge Palace in Venice years ago. I was with Jacquie and Wendy and we had one audio tour and I was designated listener/reteller. We were in a room with a ton of stuff and this very bizarre clock that ran backward and had all kinds of zodiac symbols on it. We looked at the clock and said, wow, what is that thing? And I pushed the audio tour and it took (what felt like) 15 minutes to get to the part where the guy said, "Now, look above the door, there is an unusual clock." And that was the end of it!