Video report by ITV News Correspondent Dan Rivers
The victims, all adults and one younger woman originally thought to be a teenager, were discovered in the early hours of Wednesday when the trailer was opened at an industrial estate in Essex.
Essex Police have now confirmed 31 of the victims are men, eight are women and all are from China.
In a statement, police said: "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.
"This will be a substantial operation and, at this stage, we cannot estimate how long these procedures will take."
Police said the process of moving the bodies from the lorry to a mortuary would begin on Thursday evening.
They will be driven by private ambulance under police escort from Tilbury Docks to Broomfield Hospital in Chelmsford so post-mortem examinations can be carried out.
It is hoped all the bodies will have been removed from the lorry by the weekend, a police spokesman said.
The Chinese Foreign Ministry posted a statement on its social media account saying that Chinese embassy employees in the UK were travelling to Essex to aid the investigation.
ITV News has learned more about the journey the trailer took in the days before 39 Chinese nationals were found dead.
According to an ITV News source, the trailer - which was fitted with a GPS tracker - was leased from a company in County Monaghan and driven to Lurgan in Northern Ireland on the afternoon of October 15.
It was then driven to Dublin before crossing to Holyhead in Wales.
The trailer’s journey continued to various locations in England, eventually heading to London before crossing from Dover to Calais.
It was next understood to travel through northern France and Belgium before crossing back to England, and then crossing the channel again to France and Belgium.
It eventually made its way to Zeebrugge before making the crossing back to Purfleet on Tuesday night.
ITV News understands that at no time did the trailer travel to any countries on the continent other than France and Belgium and never headed further south than Lille.
It's understood the lorry cab is owned by a company registered in Varna, Bulgaria.
ITV News Correspondent Angus Walker traced the company to an anonymous block of residential flats in Bulgaria's third largest city, which sits near the coast.
He said residents had told him a number of companies were registered there - though there is little to suggest that any company is actually being run from out of there.
He described the building as being in a run down area of the city, "a bit grey, drab".
The truck, which carries Bulgarian number plates, was first registered there in 2017 but had not been back since.
He said the address formed part of the mystery surrounding the journey of the Chinese nationals who ultimately were to be found dead.
ITV News Correspondent Peter Smith has been in the Republic of Ireland to approach those who hired the lorry trailer.
He said on Thursday night: "The trailer itself was actually registered to Dublin in the Republic of Ireland, owned by Global Trailer Rentals.
"They've released a statement to us tonight confirming that yes, the trailer is owned by them, but they say that on October 15th, they had hired out this trailer to another company.
"They've offered all this information to Essex Police, they say, including information about the tracking device that was on board.
"They have also told us that they are offering information about the company that hired the trailer from them.
"Separate to this, ITV News has learned that the trailer had been hired by another company here in the Republic of Ireland but close to the border of Northern Ireland and I approached their yard today seeking comment. I was given short shrift and told that in no uncertain terms that they had no comment to give.
"Clearly this is now an international investigation and an investigation that is very much ongoing."
Meanwhile, in the UK, police have confirmed that three addresses have been searched in Northern Ireland as officers continue to question a Co Armagh man over the discovery.
The searches in Co Armagh on Wednesday night are believed to be linked to the arrest of the driver, who ITV News understands is 25-year-old Mo Robinson, from Portadown.
He remains in custody for questioning by Essex Police on suspicion of murder. Police were on Thursday granted a further 24 hours to question the suspect.
There was no answer at the Co Armagh home of Mr Robinson's family.
Councillor Paul Berry said the village of Laurelvale, where the Robinson family live, was in "complete shock".
Mr Berry, who has been in contact with Mr Robinson's father several times, said he learned of his son's arrest through social media.
Mr Berry, who knows the father well, said the family were "very well respected" in the area.
"The local community is hoping that he (Mo Robinson) has been caught up innocently in this matter but that's in the hands of Essex Police, and we will leave it in their professional hands to try to catch the perpetrators of this."
ITV News Correspondent Peter Smith provides an update outside the driver's home
Detectives said the refrigerated trailer containing the victims arrived at Purfleet from Zeebrugge in Belgium at around 12.30am on Wednesday, while the front section came from Northern Ireland.
A spokesman for C.RO Ports, which operates terminals at Purfleet and Zeebrugge, said they would "fully assist" the police investigation.
He said: "It has been widely reported that the trailer entered the UK by ship via C.RO Ports' Purfleet Terminal, originating at our terminal in Zeebrugge.
"C.RO Ports confirms this is the case. We continue to fully assist UK, Belgian and other law enforcement authorities with their ongoing investigation.
"Our thoughts are with the family and friends of those found yesterday."
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 the Flemish TV channel VRT: "A refrigerated container in the port zone is completely sealed."
Mr Coens added: "During the check, the seal is examined, as is the licence plate.
"The driver is checked by cameras."
The Belgian federal prosecutor's office said the trailer was at the port for a short time before it was freighted to England.
The statement said it appears the container arrived in Zeebrugge on October 22 at 2.49pm local time (1349 BST), and "left the port the same day in the afternoon".
Eric Van Duyse, a spokesman for the Belgian federal prosecutor's office, said it was not yet known how long the lorry trailer spent in the country.
Mr Van Duyse said that "up till now, we have a lot of questions and not a lot of answers. We don't even know which road was followed by the truck in Belgium".
Van Duyse added: "We don't know if it stopped or not. We don't know if the people got into the container or not."
After arriving from Belgium, the lorry and trailer left Purfleet shortly after 1.05am, and officers were called 30 minutes later after ambulance staff made the discovery at the Waterglade Industrial Park.
ITV News has obtained CCTV footage of the lorry driving towards the Waterglade Industrial Park minutes before the bodies were found.
James Brokenshire, ex-Tory immigration minister, told ITV News that this was the "epitome of evil".
It was "an utterly horrific crime with people, frankly, not giving a damn about the welfare, the lives of those that they smuggled as if it is some sort of commodity", he said.
Meanwhile, David Wood, former director general of Immigration Enforcement, said that unless authorities were able to search every vehicle and container at Zeebrugge it would be difficult to determine if people had been smuggled on board.
Police originally thought the lorry had travelled to the UK through Holyhead in north Wales on October 19 but later revealed that the trailer had come directly from the Continent.
The deaths follow warnings from the National Crime Agency (NCA) and the Border Force of the increased risk of people-smuggling via Belgium and into quieter ports such as Purfleet.
The NCA previously said it had a "greater focus" on rising smuggler numbers in Belgium after the closure of a migrant camp, and a Border Force assessment highlighted Zeebrugge as being among "key ports of embarkation for clandestine arrivals".