A container filled with 31 people arrived on a ship from Zeebrugge in Belgium, police say.
The people were discovered when it was being unloaded at 7.35am by Port of Tilbury authorities.
One man has died following the discovery, while others are said to have "significant health problems".
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.