Ten teenagers were among the 39 people found dead in the back of a refrigerated lorry in Essex, police have said.
The youngest of the group were two 15-year-old boys, and the oldest was a 44-year-old man.
Essex Police confirmed that 26-year-old Pham Thi Tra, who sent a text message home saying she could not breathe, was among the victims.
The UK is working closely with the authorities in Vietnam to discuss the repatriation of those who have died.
The bodies of the 31 men and eight women were discovered on October 23.
Mo Robinson, the 25-year-old driver of the lorry, has been charged with 39 counts of manslaughter, and Essex Police are working to extradite 22-year-old Eamonn Harrison from Ireland to the UK.
Two brothers from Northern Ireland are also wanted on suspicion of manslaughter and human trafficking.
Earlier this week Vietnamese police arrested eight people in connection with the deaths.
A spokeswoman for Vietnam's Ministry of Foreign Affairs called the incident a "serious humanitarian tragedy".
The 39 victims have been named as:
Pham Thi Tra My, 26-year-old woman from Ha Tinh
Nguyen Dinh Lurong, 20-year-old man from Ha Tinh
Nguyen Huy Phong, 35-year-old man from Ha Tinh
Vo Nhan Du, 19-year-old man from Ha Tinh
Tran Manh Hung, 37-year-old man from Ha Tinh
Tran Khanh Tho, 18-year-old man from Ha Tinh
Vo Van Linh, 25-year-old man from Ha Tinh
Nguyen Van Nhan, 33-year-old man from Ha Tinh
Bui Phan Thang, 37-year-old man from Ha Tinh
Nguyen Huy Hung, 15-year-old boy from Ha Tinh
Tran Thi Tho, 21-year-old woman from Nghe An
Bui Thi Nhung, 19-year-old woman from Nghe An
Vo Ngoc Nam, 28-year-old man from Nghe An
Nguyen Dinh Tu, 26-year-old man from Nghe An
Le Van Ha, 30-year-old man from Nghe An
Tran Thi Ngoc, 19-year-old woman from Nghe An
Nguyen Van Hung, 33-year-old man from Nghe An
Hoang Van Tiep, 18-year-old man from Nghe An
Cao Tien Dung, 37-year-old man from Nghe An
Cao Huy Thanh, 33-year-old man from Nghe An
Tran Thi Mai Nhung, 18-year-old woman from Nghe An
Nguyen Minh Quang, 20-year-old man from Nghe An
Le Trong Thanh, 44-year-old man from Dien Chau
Pham Thi Ngoc Oanh, 28-year-old woman from Nghe An
Hoang Van Hoi, 24-year-old man from Nghe An
Nguyen Tho Tuan, 25-year-old man from Nghe An
Dang Huu Tuyen, 22-year-old man from Nghe An
Nguyen Trong Thai, 26-year-old man from Nghe An
Nguyen Van Hiep, 24-year-old man from Nghe An
Nguyen Thi Van, 35-year-old woman from Nghe An
Tran Hai Loc, 35-year-old man from Nghe An
Duong Minh Tuan, 27-year-old man from Quang Binh
Nguyen Ngoc Ha, 32-year-old man from Quang Binh
Nguyen Tien Dung, 33-year-old man from Quang, Binh
Phan Thi Thanh, 41-year-old woman from Hai Phong
Nguyen Ba Vu Hung, 34-year-old man from Thua Tien Hue
Dinh Dinh Thai Quyen, 18-year-old man from Hai Phong
Tran Ngoc Hieu, 17-year-old boy from Hai Duong
Dinh Dinh Binh, 15-year-old boy from Hai Phong