Mo Robinson, 25, from Portadown, County Armagh, was arrested on Wednesday by Essex Police after ambulance staff discovered the bodies in the container at the Waterglade Industrial Park in Grays earlier in the day, the BBC reported.
Officers in Northern Ireland have also raided two houses and the National Crime Agency said it was working to identify "organised crime groups who may have played a part".
The trailer arrived in Purfleet on the River Thames from Zeebrugge, Belgium.
Deputy Chief Constable of Essex Police Pippa Mills said the vehicle had been moved to a secure site at Tilbury Docks so the bodies of the 38 adults and one teenager could be "recovered while preserving the dignity of the victims".
Meanwhile, Eric Van Duyse, a spokesman for the Belgian federal prosecutor's office, said an investigation into the incident was under way.
"We have no idea at the moment how long the lorry spent in Belgium, it could be hours or days, we just don't know."
The registration for the trailer was in the name of an Irish-owned company, the Bulgarian foreign ministry said, while Prime Minister Boyko Borisov said the vehicle had not been in Bulgaria since 2017.
UK Prime Minister Boris Johnson described the deaths as an "unimaginable tragedy and truly heartbreaking."
In previous similar incidents, 58 Chinese migrants were found suffocated to death in a lorry at Dover in 2000.
In 2015, the bodies of 71 people were found in an abandoned lorry on an Austrian motorway. The police suspected that the vehicle was part of a Bulgarian-Hungarian human trafficking operation.
( With inputs from IANS )