A group of 35 men, women and children found inside a shipping container at a port are understood to be Sikhs from Afghanistan, Essex Police say.
They were discovered on Saturday morning after a freighter arrived at Tilbury Docks from Belgium.
The police force has described them as victims of "people trafficking".
One man was found dead inside the container and the others were taken to hospital to be treated for severe dehydration and hypothermia.
Officers are working with Interpol and other international authorities to try to establish what happened.
Police are questioning some of the survivors and have also launched a homicide investigation following the man's death.
Thirty of the migrants have been released from hospitals and are now in the care of Essex Police and Border Force staff.
Four remain at Southend Hospital. It is thought they will be discharged later on Sunday.
Superintendent Trevor Roe of Essex Police said: "The welfare and health of the people is our priority at this stage.
"Now they are well enough, our officers and colleagues from the Border Force will be speaking to them via interpreters so we can piece together what happened and how they came to be in the container.
"We now understand that they are from Afghanistan and are of the Sikh faith.
"We have had a good deal of help from partners within the local Sikh community in the Tilbury area to ensure that these poor people, who would have been through a horrific ordeal, are supported in terms of their religious and clothing needs."