"We believe that a number of other people traveled into the U.K. in a similar way to the 39 deceased throughout the month of October, and we hope that these people would be able to help us," Police Assistant Chief Constable Tim Smith, who works in Essex where the truck was found, said in a statement on Wednesday.
"We understand that there may be concern about coming forward and sharing their experiences, but we can assure you that your information and details will be treated in confidence."
There were no explicit assurances they will not be deported, however.
The appeal is part of the ongoing probe into the deaths of the 39 Vietnamese who died in a refrigerated container truck last October in a tragedy that shocked the world.
Last month the Essex police wrapped up post-mortems, revealing the provisional cause of death was a combination of hypoxia and hyperthermia.
Earlier this week they detained Alexandru-Ovidiu Hanga, 27, in connection with the deaths, charged him with an immigration offense and produced him in court on Wednesday. Last month they had arrested two others on suspicion of involvement in the deaths.
Police in the north-central province of Ha Tinh, home to 10 of the victims, also arrested seven people last month and were looking for another. Last year police arrested 11 people in Nghe An and Ha Tinh provinces on suspicion of human trafficking.
The youngest of the 39 killed were boys aged 15 and the oldest was 44.
Their remains were brought home a month after the tragedy.
Of the 39 victims, 21 were from Nghe An, 10 from Ha Tinh, and the rest from Quang Binh, Thua Thien-Hue, Hai Duong and Hai Phong.
Vietnam is consistently one of the top source countries for modern slaves in Britain, with at least 3,187 Vietnamese victims being identified since 2009, according to official data.
Victims trafficked from Vietnam most commonly end up being exploited, often in cannabis farms and nail bars, but many are also sexually exploited.