Police were called by the ambulance service shortly before 01:40 BST after the discovery at Waterglade Industrial Park in Eastern Avenue, Grays.
The lorry driver, a 25-year-old man from Northern Ireland, has been arrested on suspicion of murder.
Early indications are that 38 adults and one teenager have died, Essex Police are in the scene as investigations are continuing.
Initial reports suggest the victims are from Bulgaria and human trafficking may be involved in a snuggling ring coming through Wales.
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