The driver, an Irish man in his 50s, has also been arrested on suspicion of assisting the men, local Wiltshire Police said in a statement.
The men are aged between 16 and 30. Their nationalities are unclear, officers said.
One of the men was initially taken to hospital as a precaution, but later released. They are “fit and well” and now in custody, police added.
A member of the public alerted police to the truck, which was traveling on a highway near the town of Chippenham at around 8.30 p.m. local time (3.30 p.m. ET) Wednesday evening.
The discovery come weeks after dozens of people, thought to be Vietnamese, were discovered dead in the back of another truck east of London, shining a spotlight on people smuggling in the UK.
The driver of that truck, Maurice “Mo” Robinson, 25, appeared in court last month charged with 39 counts of manslaughter.
British police investigating the deaths have also appealed to two brothers — Ronan Hughes, 40, and Christopher Hughes, 34 — to hand themselves in.
The brothers, from Armagh in Northern Ireland, are believed to have links with the road haulage and shipping industries, and are wanted on suspicion of manslaughter and human trafficking.
“I fully understand that recent tragic events elsewhere in the country will mean there will be increased interest and heightened concern regarding this incident,” said Wiltshire’s duty superintendent, Steve Cox, about the most recent truck discovery.
He also applauded the “vigilant member of the public who initially reported this incident to us — it is thanks to them that this incident was resolved swiftly and safely with no serious casualties.”