An allegorical fable is a story told to represent another instance in time with several symbols and levels of association between the two storylines.
Golding claims to have written this as a response to a book called Coral Island: A Tale of the Pacific Ocean. The work demonstrated the truth of that which most children believe: a world without adults is a superior world. This may be a major reason Golding decided to try to write in a parallel format, he saw a world going through tremendous trial, fear, and chaos which had great need for reformers.
Many teachers and students today look at the work as a parallel to regular societies that with the removal of our civilized infrastructures might revert to barbarianism. The "Lord of the Flies" represent the Devil himself and given the circumstances to leave the comfort of our present situations, many hypothesize that Golding was saying we would go about a violent means to achieve our own selfish aims.
Thus, is this a real allegorical fable? Maybe. It seems there are many symbols that represent either society or a fight between good and evil. There are even some direct references Golding himself applied to insist there is connection to another resource. However, I think it is up to the reader to draw several connections from one source to another. I would assert that this is not near the allegorical fable that Animal Farm has become. Those connections are obvious and blatant. The conclusions are also very simply drawn. These connections are a bit more of a stretch in Lord of the Flies.