Police have said they have 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 lorry trailer at Waterglade Industrial Park in Grays on 23 October - were from Vietnam.
Essex Police said a series of files had been brought before an identification commission with the assistance of police officers in Vietnam, adding that the victims' families had all been told.
HM Senior Coroner Caroline Beasley-Murray said: "May I take this opportunity to offer my deepest condolences to the victims' families."
Assistant Chief Constable Tim Smith, of Essex Police, said: "This is an important step in the investigation and enables us to work with our Vietnamese Police colleagues to support the families of those victims.
"It is only right that we provide an opportunity for family members to take in the news confirming the death of their loved ones before releasing any further information. Our thoughts remain with the families and friends of those whose tragic journey ended on our shores."
The Vietnamese embassy in London said in a statement it was "in deep sorrow" over the deaths of the 39 Vietnamese nationals.
"Once again, we would like to convey our profound condolences and sympathy to the bereaved families," it said.
The embassy said it would continue to work with the relevant agencies in Vietnam and the UK "to provide consular protection and support for the bereaved families in order to bring their loved ones home at the earliest time".
Vietnamese authorities had previously believed that the victims were all from the country, and released a statement at the weekend expressing sadness over the deaths.
The investigation into the deaths is ongoing, with the most recent development on Monday, when eight people were arrested in Vietnam over the incident.
Two have so far been charged.
British police have also begun extradition proceedings against Eamonn Harrison, 22, from Newry in Co Down, Northern Ireland.
He appeared at Dublin Crown Court last Friday charged with 39 counts of manslaughter, as well as human trafficking and immigration offences.
He has been remanded in custody.
The alleged driver of the lorry, Mo Robinson, 25, appeared at Chelmsford Magistrates Court last week, charged with 39 counts of manslaughter, as well as further related offences.
Essex Police have made a direct appeal to two other suspects.
Officers said they had spoken to one of the men, Ronan Hughes, 40, by phone. He is wanted along with his brother, 34-year-old Christopher Hughes, on suspicion of manslaughter and human trafficking.
From Armagh in Northern Ireland, they also have links to the Republic of Ireland, and to the road haulage and shipping industries.