Eleven people, including six children, were found locked in the back of a lorry in a lay-by.
Firefighters cut the locks after police were called to reports of banging from inside the vehicle, which was parked at Willoughby Hedge on the A303 at West Knoyle on Saturday afternoon.
The Home Office said immigration enforcement officers found 10 Iraqi nationals and one Afghan national.
Police said the driver was helping with inquiries but had not been arrested.
The driver of the lorry had been returning to Taunton from Belgium and had stopped for lunch at a roadside cafe.
David Thomas, who runs the cafe, said the driver could not open the back doors because they had been glued shut.
He said the occupants had been "pretty lucky" because part of the lorry was refrigerated.
"The compartment they were in contained a few pallets of rather expensive Belgian chocolate and was at a normal temperature," he said.
"I understand from the driver if they'd been in the front compartment that was quite well-chilled so they would have had a few problems there."
A Wiltshire Police spokesman said the adults found in the lorry were being kept in custody overnight and would be handed to Home Office officials on Monday.
"We are currently working with colleagues from the Home Office Immigration Department as our inquiries progress," a spokesman said.
"Where someone has no right to remain in the UK, we will take action to remove them," a Home Office spokeswoman added.
Wiltshire Council said it was working with its partner agencies "to provide support and help to those involved".