Police are expected to begin questioning some of the people found in a shipping container at a port.
A man died and 34 people - including children - were taken to hospital after they were rescued from the container at Tilbury Docks, when staff heard "screaming and banging" on Saturday morning.
The survivors - described as victims of "people trafficking" - were suffering from severe dehydration and hypothermia.
Police have launched a "homicide investigation" into the man's death and are working with other international authorities to establish the circumstances of the incident.
Officers said interpreters had been brought in to help with the "language issues", as they begin to speak to the group, who are believed to be from the Indian subcontinent.
The uncle of dead Afghan immigrant Meet Singh Kapoor says he wanted a better life for his children. Instead his children watched him die.
ITV News has spoken to the translator police used after 35 Afghan Sikhs, including 13 children, were found in a boat in Tilbury Docks.
ITV News has obtained exclusive footage of people, believed to be Afghan Sikhs, being released from a shipping container at Tilbury Docks.