They probably close the terminal overnight for a few hours to keep Southend's tramps and homeless from dossing in the warm rather than any commercial reason.
It must be a strange experience arriving at a London Airport and finding the front doors locked while the cleaners go about their business.
Many passengers like to arrive late at night for early morning departures which can make terminals look somewhat untidy with people kipping on the floor in sleeping bags but airports seem to put up with it.