Hoang Van Tiep, 18, and Nguyen Van Hung, 33, were among the first of 16 of the victims repatriated to Vietnam on Wednesday (November 27).
The two were cousins and their families lived next door to each other in the rural town of Dien Chau.
Vietnamese and British authorities continued to coordinate to repatriate the remaining bodies, it added without giving further details.
Police in Vietnam have arrested 10 people in connection with the deaths. On Monday (November 25), the British driver of the truck admitted plotting to assist unlawful immigration and acquiring criminal property.
The grisly discovery of the bodies on October 23 in an industrial estate near London, a magnet for Vietnamese migrants, has shone a spotlight on the people-smuggling trade bringing the poor of Asia, Africa and the Middle East on perilous journeys to the West.