Essex Police said inquiries would continue after a post-mortem examination carried out on the body of Meet Singh Kapoor, 40, from Afghanistan, proved inconclusive.
Thirteen children aged as young as one were among the Afghan Sikhs rescued from the shipping container on Saturday.
Members of the 35-strong group found screaming and banging after arriving at the Port of Tilbury, Essex, from Belgium, have finished speaking to police and are now being cared for by Home Office officials
Superintendent Trevor Roe said: "Tragically, one man died on the voyage and the investigation into his death is now being led by us.
"These people were found in an awful situation and our priority is to look after them."
Kamaljit Singh Mataharu, a translator used by police, said the group believed they would have died if they remained trapped for another 30 minutes. He added they told him: "It was pitch black, without any air."
Mr Mataharu said there were 15 families, all from Kabul, in the container after they travelled to Europe in a lorry. They told him they had been in the container for 18 hours. There were nine men and eight women aged 18-72, and 13 children.