As of Sunday, 24 families in Nghe An and its neighbor Ha Tinh Province have reported missing members in the United Kingdom and Europe.
Yesterday, Deputy Chief Constable Pippa Mills said: "This is a fast-moving investigation involving significant police resources dedicated to finding out the truth about what happened to the 39 people found dead in the lorry on Wednesday".
Boris Johnson wrote in the book Monday at the Thurrock Council office that "the whole nation, and indeed the world, has been shocked by this tragedy".
Central Vietnam has always been a source of illegal migration to Britain for people seeking better lives. He plans to place a wreath in remembrance.
UK Prime Minister Boris Johnson, who campaigned for stronger borders while pushing Britain to leave the European Union in the 2016 referendum, signed a book of condolence Monday and laid flowers in Grays, east of London, where the truck was found.
Pictured is one of the victims who is understood to have been onboard the container were 39 people where found dead in Essex on Wednesday morning.
He is due to appear at Chelmsford Magistrates' Court tomorrow.
The vehicle, stopped near the border with Lithuania, was being driven by a 44-year-old Polish national transporting wood. Five people are being questioned by police, including the truck driver and three people who were arrested Friday on suspicion on manslaughter and conspiracy to traffic people.
Robinson made no application for bail.
Police said their investigation includes over 500 exhibits, including mobile phones which have to be downloaded to help identify the victims.
A Catholic priest in the remote town of Yen Thanh in Nghe An province said on Saturday that he believed most of the dead were likely from Vietnam, where remote communities have been plunged into mourning.
Essex Police initially believed the victims were all Chinese nationals.
The mother of missing 28-year-old man Vo Ngoc Nam said she last heard from her son days before the container was found.
The Vietnamese embassy in the United Kingdom is working to "accelerate the process of confirming the victims' identities", according to a statement from the foreign ministry in Hanoi.
"It's a cruel stage for the families, because hundreds if not thousands are now on those routes, so I appreciate we are getting calls from Vietnam saying my loved one is missing and my loved one may be on that lorry (truck), but they could be on another lorry", he said.
Officials started collecting DNA samples from families in Nghe An and Ha Tinh, impoverished provinces in central Vietnam where most of the suspected victims came from.
It was not immediately clear what type of documents were sent.
United Kingdom police are struggling to identify the victims, who are believed to have come from Asia, and autopsies are being performed.
In Vietnam, a number of families told AFP news agency that their relatives had gone missing on route to Britain. He was the first of those arrested to be charged in what is seen as one of the U.K.'s biggest cases of people smuggling.
China's Assistant Foreign Minister Chen Xiaodong said the case shows that illegal immigration is a global issue. She is said to be the legal owner of the truck.