Essex Police said yesterday they believed the victims were Chinese nationals - but sources close to the investigation say a number are thought to be Vietnamese, The Telegraph reports.
Tra My had been attempting to get into the UK when she text her mum on Tuesday at the same time the doomed trailer was on its way to Essex from Zeebrugge in Belgium.
She wrote: "I’m sorry Mum, my path to abroad didn’t succeed.
"Mum, I love you and Dad so much! I’m dying because I can’t breathe.”
Her family haven't heard from her since, with a spokesperson from the Vietnamese Embassy in the UK confirming Essex Police had been in contact.
They are said to have paid £30,000 for her to be smuggled into Britain, the BBC reports.
Hoa Nghiem of Human Rights Space in Hanoi posted a picture of Tra My on Twitter with a plea for information.
She said: "My's family has asked for help. The person told me there were six other people asking for similar assistance to fund out whereabouts of their relatives or family member since they also lost contact since October 23.
"We don't know if that would make six cases as we are verifying names. And we don't know if they are in that Essex truck. We hope they are not.”
Tra My had reportedly gone to China in early October in the hope of travelling to the UK via France for a better life.