The 29 people found in the back of a van stopped by police on the M5 are thought to be Vietnamese, officials say.
Devon and Cornwall Police arrested four men aged 55 to 72 after being called to Newlyn, Cornwall, on Friday after people were seen getting into the back of a van from a boat.
The van was stopped near Cullompton, in Devon, at about 09:00 BST.
Police said a mix of men, women and children were among the 29 people.
A force spokesman said: "They currently remain in a specially-created centre where they are being taken care of."
The four men arrested on suspicion of immigration and modern slavery offences, including human trafficking, were a 72-year-old and a 55-year-old from Lancashire and a 63-year-old and a 62-year-old from Kent.
Police said they had gained custody extensions on all four suspects, who remain in custody awaiting further questioning.
'Supporting the group'
A spokesman for Devon Children and Families Partnership said agencies in Devon and Cornwall were supporting the group and arrangements for temporary accommodation will be made if any of the individuals are under 18 years of age, pending further decisions about their status.
He added: "The UK Government will decide what the next steps will be for these individuals."
A British Red Cross spokesperson added: "Our volunteers are continuing to support a number of people who are the alleged victims of human trafficking.
"We are providing them with practical and emotional support at a rest centre while the police conduct their investigations.
"Our volunteers are neutral and impartial and are concerned only with the welfare of the people affected."