Police in Vietnam took hair and blood samples on Sunday to identify the 39 people who died in a truck trailer in Essex, east of London.
According to Reuters, fathers of missing Vietnamese individuals said local police took their samples.
The fathers added they lost contact with children after they received messages saying things like they were running out of air.
Police initially believed the deceased were Chinese, but now up to 25 victims are thought to have come from the same farming village in Vietnam.
Chinese and Vietnamese authorities say they are working closely with British police.