According to Shadowman's recollection, there was a small group of children who originally lived there at the very beginning of the disaster. They were joined by the Notting Hill group which included Shadowman, Jester, and Rose. Later it was David, Pod, and the redcoat guards that joined and took power.
The palace is divided into groups of kids based on their chores. David is king while Jester is his second in command. Pod is third in command and leader of the redcoat guards. Underneath the guard group are the gardeners, cooks, and other laborers. There are not many fighters, as shown by David's interest in using the Holloway group as his mercenaries.
The palace kids themselves have few qualms about who they are allied with but David has a strong dislike of the Tower and Natural History Museum groups. He allies with the Westminster Palace kids and the Squatters are temporarily put under his control.