Eight of the victims are women and 31 are men. All are adults.
One female victim was previously thought to have been a teenager. Officers said she is a “young adult woman”.
Police have begun the process of moving the bodies from the lorry to a mortuary.
The first 11 victims are being transported under police escort by private ambulance from the Port of Tilbury to Broomfield Hospital in Chelmsford, having left the port at 7.41pm.
Staff from the Chinese embassy in London are expected to visit the scene where the bodies were found, the AFP news agency reported.
An embassy spokesperson said: “We read with heavy heart the reports about the death of 39 people in Essex, England.
“We are in close contact with the British police to seek clarification and confirmation of the relevant reports.”
The developments emerged as detectives were granted an extra 24 hours to question the vehicle’s 25-year-old driver, who was arrested on suspicion of murder.
Authorities found the 39 bodies when the lorry was stopped at an Essex industrial estate in the early hours of Wednesday.
The discovery echoes a similar case in 2000 when 58 Chinese citizens were found dead in a sealed, airless container at Dover.
The addresses are believed to be linked to the lorry driver, named in reports as Mo Robinson from Portadown.
Authorities have not named the driver and he has not been charged with a crime.
“We want to be clear – we have not speculated about the identity of this man, and we will not do so,” an Essex police spokesperson said.
Paul Berry, a local councillor, said the village of Laurelvale, where the Robinson family live, was in “complete shock”.
He said Mr Robinson’s father learned of his son’s arrest through social media.
The 25-year-old remains in police custody.
Detectives said the trailer containing the victims arrived in the UK at Purfleet, from Zeebrugge in Belgium, at around 12.30am on Wednesday.
The front section to which it was attached, known as the tractor, came from Northern Ireland.
“The tractor unit of the lorry had entered the country via Holyhead on Sunday 20 October, having travelled over from Dublin,” an Essex Police spokesperson said.
“The lorry then collected the trailer, which had travelled from Zeebrugge, at the port of Purfleet at around 12.30am on 23 October. The cab and trailer left the port shortly after 1.05am.”
Belgium’s federal prosecutor’s office said the lorry was only in the country for a short time as it passed through the port of Zeebrugge.
Cooling containers often move swiftly through the North Sea port, often just with a visual check, for the short crossing to England.
Experts said temperatures in refrigerated lorry units can be as low as -25C.
Joachim Coens, chief executive of Zeebrugge port where the lorry trailer departed from, said it was unlikely people were loaded into the container at the Belgian site.
He told Flemish TV channel VRT: “A refrigerated container in the port zone is completely sealed.
“During the check, the seal is examined, as is the licence plate. The driver is checked by cameras.”
Detectives are investigating whether organised criminal gangs could be behind the deaths. Fears are growing that the case could become one of Britain’s worse people-smuggling tragedies.
Authorities moved the lorry and the container to Tilbury Docks so the bodies could be recovered while preserving the victims’ dignity.
“Each of the 39 people must undergo a full coroner’s process to establish a cause of death, before we move on to attempting to identify each individual within the trailer,” a police spokesperson said.
“This will be a substantial operation and, at this stage, we cannot estimate how long these procedures will take.”
Simon Coveney, the deputy Irish premier, said the country’s police force, the Garda Siochana, would cooperate fully with the investigation.
“This is an issue that comes right into our own lives, into the UK and the investigation that’s under way at the moment involves Garda Siochana,” he said.
“The investigation taking place will have the absolute and full cooperation of an Garda Siochana.”
Hours after the bodies were discovered on Wednesday, police in Kent found nine people alive in the back of a lorry on the M20.
A further six people were found alive in the back of a second vehicle also driving down the London-bound carriageway on Wednesday afternoon.
The discoveries come as the National Crime Agency (NCA) said the number of migrants being smuggled into Britain in lorries has risen in the last year.
The NCA has previously warned that it suspects criminal networks of targeting quieter ports on the east and south coasts of the UK, such as Purfleet.
A Border Force assessment had also highlighted Zeebrugge as among the “key ports of embarkation for clandestine arrivals”.
The Independent has contacted the Chinese embassy in London for comment.
Additional reporting by agencies