How does that fact that the characters went to private school impact the novel Lord of the Flies, by William Golding?
This is an excellent question. William Golding's Lord of the Flies is set on an isolated tropical island, and the characters are all English schoolboys who landed there during an airplane crash. Most of the boys did not know one another before they arrived on the island; the notable exception is the choir, which is probably why they develop into a hunting pack so quickly.
The fact that they all attended all-boys boarding schools (private schools) probably contributes to the boys' merciless teasing of Piggy, the only boy among them with physical "defects." He is fat, asthmatic, and wears glasses--all of which make him an easy target for ridicule. This is undoubtedly a practice they learned and practiced while at school, for all of them contribute to the taunting without any prompting. (Conversely, they choose Ralph as their leader based solely on his physical appearance, which confirms the fact that their opinions about people were determined, at least initially, by what they see.)
All the boys lived at boarding schools away from their parents, so even the youngest ones (five- and six-year-olds, referred to as the littluns) are used to sleeping in unfamiliar places and being rather self-sufficient. Before long, however, these boys begin to have nightmares. They see things in the dark and are afraid. Later, even the older boys, presumably quite used to sleeping away from their families, also have nightmares and bad dreams. Golding uses this to create a mood of fear among the boys on the island.
Finally, Golding uses the image of uniformed, polite, and rule-following English schoolboys (is there anything more proper, really?) as a stark contrast to what they become by the end of the novel-- savages. When they are finally discovered by a uniformed naval officer, he sees Ralph and then "other boys appearing now, tiny tots some of them, brown, with the distended bellies of small savages." In fact, for most of the last chapter of the novel, as every boy on the island tries to kill Ralph, they are not referred to by name but by the general term "savage."
If, say, the characters in this story had been a group of strangers who had simply been on the plane when it crashed, the story would still have had impact; however, because they were young English schoolboys, their descent into savagery is even more pronounced and therefore more powerful.