Post-mortem examinations are due to be carried out on some of the 39 people found in a refrigerated lorry in Essex.
Eleven of the victims were taken by ambulance from the Port of Tilbury to Broomfield Hospital, Chelmsford on Thursday evening.
Police, who are still questioning the lorry driver on suspicion of murder, believe the victims were Chinese.
GPS data shows the container crossed back and forth between the UK and Europe in the days before it was found.
The BBC understands that full details of the tracking data have been passed to Essex Police.
The force has been given extra time to hold driver Mo Robinson, 25, who was arrested on Wednesday.
Police said recovering the bodies of the 31 men and eight women would take time and the dignity of the victims was its primary concern.
The Chinese Ambassador to the UK, Liu Xiaoming, said he had sent a team to Essex to help verify the identity of the victims. He added that their nationality was yet to be confirmed.
Three properties in Northern Ireland have been raided and the National Crime Agency is working to establish if "organised crime groups" were involved.
Police believe the tractor unit - the front part of the lorry - arrived at Holyhead in north Wales on Sunday, having travelled from Dublin.
The trailer arrived in Purfleet on the River Thames from Zeebrugge in Belgium at 00:30 BST on Wednesday.
The lorry and trailer left the port at Purfleet shortly after 01:05 the same day and the bodies were found in the container at Waterglade Industrial Park in Grays about 30 minutes later.
Purfleet has been described as a "magnet" for illegal immigrants by locals.
Janet Lilley, 61, said about a decade ago she started to notice people "wandering around with suitcases and backpacks".
"Over the last few years it's got worse," she said.
"People would come strolling out of the docks, get in the vans and that's it, they drive off."
Mrs Lilley described seeing pages of torn-up passports blowing into her garden.
Lee Tubby, 45, who lives opposite the port, said he has seen people "climbing out the top and out the back" of lorries.
Global Trailer Rentals Ltd told RTE News that it owned the trailer and said it had been hired on 15 October.
Sources say an outline of tracking data shows the container left GTR's yard in Carrickmacross in County Monaghan in Irelandthat day and crossed into Northern Ireland before returning to the Republic of Ireland.
The data shows it then travelled to Dublin and crossed over to Wales overnight on 16 October, before going to Europe on the Dover to Calais route that evening.
Once in Europe it appears the container travelled between cities in Belgium and France, including Dunkirk, Bruges, and Lille.
Belgian authorities have said it is "highly unlikely" the victims got into the container at Zeebrugge.
Dirk De Fauw, chairman of the port of Zeebrugge and mayor of Bruges, told VRT News: "Breaking the seal, putting 39 people in a trailer and resealing the trailer without anybody noticing is virtually impossible."
China's ambassador to the UK, Mr Liu, tweeted: "The Chinese Embassy has sent a team led by the minister-counsellor in charge of consular affairs to Essex, England.
"They have met with the local police, who said that they are verifying the identity of the 39 deceased, whose nationality still cannot be confirmed."
The deaths follow warnings from the National Crime Agency and Border Force about the increased risk of people-smuggling using quieter ports such as Purfleet and routes through Belgium.
It also emerged the Home Office was warned two years ago that Border Force had staffing problems at east coast ports including Purfleet, where the container containing the 39 Chinese nationals docked.
An inspection report in July 2017 from David Bolt, The Chief Inspector for Borders and Immigration, said that although Border Force was coping, it was "stretched".
In some instances, he said it was " too thinly" stretched.
The chief inspector also criticised the lack of strategic management by Border Force of its relationships with the companies who own and run the ports, the BBC's Home Affairs Correspondent, Danny Shaw, reports.
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