Buckingham Palace is the residence of the Queen of England. No matter what time of the day you show up at the palace gates, it will be packed. Although the iron gates always stay bolted shut, a glimpse at the Queen's residence is enough to have you gaping. Plus, the change of guard is something worth checking out, though I'm not too sure of the exact time of day it happens.
There are loads of things to keep you busy - there is a Speakers Corner if you are keen to hear people speak, boating and swimming in the lakes, Kensington Palace on one end which is now a museum to Diana, two cafes (Lido and Serpentine again I think), sunbeds to sit out in the sun, or you can just run/roller blade around the park for a total of 7 kms!