.... you RUN WITH the changing guard! (Think the running of the bulls in Pamplona, with less danger of being gored....).
We met up the the old guard at St. James Palace and sprinted/dashed/weaved our way through the Mall running right alongside them, all the way to the gates of Buckingham Palace. Then, as they made their way through the gates, we dashed around to Wellington Barracks just in time to see the new guard march out and sprinted alongside them. Those that were still standing, ran up the stairs to a ramparts vantage point with a spectacular overview of the proceedings.
(Disclaimer: For those of you saying to yourself, "That doesn't look particularly strenuous", that is because during the maddest dashes the video needed to be turned off so that we could REALLY run. I highly recommend a getting stress test before attempting this maneuver.)