The driver of the truck, named locally as 25-year-old Mo Robinson, from Northern Ireland, remains in custody after he was held on suspicion of murder.
Essex Police said on Friday that a man and a woman, both aged 38 and from Warrington, Cheshire, were arrested on suspicion of 39 counts of manslaughter and people trafficking.
An international investigation is under way as post-mortem examinations are due to begin on the bodies found in a refrigerated trailer in Grays in the early hours of Wednesday.
On Thursday evening, the first 11 bodies were moved by a private ambulance with a police escort from the port of Tilbury to Broomfield Hospital in Chelmsford.
Police have not confirmed whether the driver raised the alarm after finding the eight women and 31 men, who are all believed to be Chinese nationals, while his supporters have set up petitions online calling for his release.
People living close to Purfleet - the port where the container entered the UK - said illegal migrants were a familiar sight.
"It's a magnet for illegals," said Janet Lilley, 61. "People would come strolling out of the docks, get in the vans and that's it, they drive off."
Lee Tubby, 45, who lives opposite the port, said he has seen people "climbing out the top and out the back" of lorries and cutting the plastic roof covering to climb through.
"We've had people just come out of the port knocking on the door asking for shoes, asking for water," he said.
It is not yet known when the victims entered the sealed refrigerated trailer, where temperatures can be as low as -25C, or the exact route it travelled.
Mike Gradwell, a former Lancashire Police detective superintendent who worked on the probe into the Morecambe Bay cockling tragedy in which 23 Chinese illegal immigrants drowned, told BBC Breakfast that those inside could have been trafficked by a Snakehead gang.
"These are criminal travel agents really - you go to a Snakehead to say you want to be trafficked to an economic opportunity and usually you'll borrow quite a significant amount of money," he said.
Belgian officials said the trailer arrived at Zeebrugge at 2.49pm on Tuesday and left the port the same day en route to Purfleet.
Joachim Coens, chief executive of Zeebrugge port, said it was unlikely people were loaded into the container at the Belgian site, while Mayor Dirk De Fauw, who is also the chairman of the port, said it was "virtually impossible" the victims went into the trailer at the Belgian border.
The trailer arrived at Purfleet at around 12.30am on Wednesday, and the front section to which it was attached, known as the tractor, came from Northern Ireland via Holyhead in North Wales on Sunday.
The lorry and trailer left the port at Purfleet shortly after 1.05am, and officers were called to the Waterglade Industrial Park on Eastern Avenue in Grays at 1.40am.
Irish company Global Trailer Rentals Ltd (GTR) confirmed it owned the refrigerated part of the lorry and a spokesman said the company was "shellshocked" and "gutted" by the news.
The firm said the trailer had been leased on October 15 from its rentals yard in Co Monaghan, in the Republic of Ireland, at a rate of 275 euro (£237) a week.
It said it provided police with information about the person and company that leased the trailer, as well as offering to make tracking data available.
Three addresses have been searched in Northern Ireland as part of the probe, while warrants were also carried out in Cheshire.
China has called for joint efforts to counter human smuggling, while vigils have been held in London and Belfast to pay tribute to the victims.