A lorry driver from Ireland, arrested in connection with 15 people believed to have been entering the UK illegally, has been released on bail.
The stowaways were discovered leaving a refrigerated trailer on the A350 near junction 17 of the M4 on 6 November.
The Home Office said the people were Iraqi and Iranian nationals and were being held in custody.
Immigration Enforcement was contacted by police officers who attended the scene near Chippenham.
The driver, a man in his 50s from Ireland, was arrested at the scene.
Wiltshire Police said it was alerted by a call from a member of the public at about 20:30 GMT. Emergency crews attended the A350 and a road closure was put in place.
Paramedics said all of the suspected migrants were male and aged between 16 and 30.
One man was briefly taken to hospital but he is now in custody.
A spokesman for the Home Office said: "The investigation is still ongoing and individual cases will be dealt with according to the Immigration Rules."