Frank Walling, 72, and Glen Bennett, 55, pleaded guilty to two charges under the Modern Slavery and Immigration Acts at a trial on Tuesday, the Metro news site reported.
The pair were arrested on April 12 after police stopped two vans where 29 Vietnamese nationals, including children, were found crammed inside the back of the vehicles in the County of Devon to the southwest of England. The Vietnamese had arrived on a fishing boat, police found.
The duo were remanded to custody and will return to for trial on October 11 when they will be sentenced.
Vietnam is consistently one of the top source countries for modern slaves in Britain - at least 3,187 Vietnamese victims have been identified since 2009, according to official data.
About 362 possible child victims from Vietnam were discovered in Britain in 2017, up more than a third over 2016.
Victims trafficked from Vietnam most commonly end up being exploited, often in cannabis farms and nail bars, but many are also sexually exploited, according to a report commissioned by Britain’s Independent Anti-Slavery Commissioner Kevin Hyland.