The Changing of the Guards captured by the LC-A.
It doesn’t get more British than this. :) The Changing of the Guards (or Guard Mounting) is the best thing to see at Buckingham Palace. You can see the Changing of the Guards any day from May to June, the ceremony takes place at 11:30 am (if you plan to go at another time of the year, check online to see on which day the Changing of the Guards will take place). The ceremony will last for 30 minutes. Get there early if you want a good spot for pictures.
You can also see Guard Mounting at Windsor Castle, the ceremony also takes place at 11:00 am and you can see it any day from April to July.
WARNING: There’s no Guard Mounting during very wet weather conditions (a very useful bit of information to have when you live in London).