Police said they formally identified all 39 bodies that were found in a trailer in Essex last month.
Vietnamese police also confirmed that all the victims – who were found in a refrigerated truck at Waterglade Industrial Park in Grays on October 23 – were from Vietnam.
Essex police said a series of files were presented to an identification committee assisted by police in Vietnam, adding that all the victims' families were informed.
Waterglade Industrial Park in Essex where the trailer was found
Caroline Beasley-Murray, senior coroner for HM, said, "I can take this opportunity to offer my deepest condolences to the families of the victims."
Essex Police Chief of Police Assistant Tim Smith said: "This is an important step in the investigation and allows us to work with our colleagues in the Vietnamese police to support the families of these victims.
"It is only fair that we offer family members an opportunity to receive news that confirms the death of their loved ones before disclosing more information. Our thoughts remain with the families and friends of those whose tragic journey has ended behind us."
The Vietnamese embassy in London said in a statement it was "deeply saddened" by the death of the 39 Vietnamese citizens.
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"Once again, we would like to convey our deep condolences and sympathy to the bereaved families," it said.
The embassy said it would continue to work with relevant agencies in Vietnam and the United Kingdom "to provide consular protection and support to bereaved families in order to bring their loved ones home as soon as possible."
"There were 100 people on their way to new lives"
Vietnamese officials previously believed the victims were all from the country and issued a statement over the weekend expressing sadness over the deaths.
Investigation into the deaths is ongoing, with the latest development on Monday, when eight people were arrested in Vietnam over the incident.
So far, two have been charged.
British police have also launched an extradition case against Eamonn Harrison, 22, of Newry in Co Down, Northern Ireland.
He appeared at the Dublin Crown Court last Friday on 39 counts of manslaughter, trafficking in human beings and immigration crimes.
He was arrested in custody.
Essex Police Appeal to Wanted Men
The alleged driver of the truck, Mo Robinson, 25, appeared at Chelmsford Magistrates Court last week on 39 counts of manslaughter and other related offenses.
Essex police appealed directly to two other suspects.
Police said they had talked to one of the men, Ronan Hughes, 40, by telephone. He is wanted along with his brother, Christopher Hughes, 34, on suspicion of wrongful death and human trafficking.
From Armagh, Northern Ireland, they also have links to the Republic of Ireland and the road transport and shipping industries.