Everyone knows about the Changing of the Guard at Buckingham Palace, daily at 11:30. It is so crowded that you can hardly see what is happening. Skip that, and instead see the better show at the Guards' Barracks on Birdcage Walk at 11 a.m. when the guard is inspected before going to the Palace for the change ceremony. Few people know about it, so you can always get a good view. First, the regular troops march out and line up for inspection. Shortly, the band guys in the bearskin hats muster and march out. They march around in a circle for a bit, then stand at attention for inspection. Then they play a bit of music. The day I saw it, they played the theme from "Indiana Jones," which I'm sure must also be a classical composition appropriated by ol' Indy for the movies. It was very stirring. An older gentleman next to me explained that today's band was the Gloucestershire Regiment, known as Glorious Gloucestershire. They marched around a bit more. Then three mounted police officers appeared outside the barracks' gates, traffic was stopped, and the bearskin hat guys struck up a rousing march and all trooped out the gate and across the street to the palace for the famous Changing of the Guard. Of course, the entire spectacle was made more enjoyable by the knowledge that I was seeing something that few other tourists knew about, and I did not have to fight the crowds to see.
The Wellington Barracks are on Birdcage Walk, across from St. James Park, opposite Spur Road, about 500 yards from Buckingham Palace. The inspection is on the "parade ground" which is also the barracks parking lot. Nearest tube: St. James Park on the Circle and District lines.