Historical Context

Lord of the Flies takes place during a war, but it is never said what sort of war is going on.

World War 2
While unlikely, it is possible that this book takes place during World War 2, due to the time the novel was published in, and because of its implications of older times. One might take this as an alternative version of World War 2, as it is said that a nuclear bomb exploded in England, something that did not happen in the real World War 2.

World War 3
More likely than the previous postulation is the possibility that this takes place during a hypothetical World War 3. This is supported by the fact that England was not bombed during World War 2, but could be bombed during World War 3.

A smaller war
A possibility that most might not consider is that this could be a smaller war not involving the rest of the world. However, a nuclear exchange between two countries would easily provoke other nations to defend their allies and therefore join in the fighting, which could easily escalate into a third World War.