The bodies of 38 adults and one teenager, who are believed to be of both men and women., were discovered in a lorry on the Waterglade Industrial Park near Grays on Wednesday morning.
A 25-year-old man from Co Armagh, Northern Ireland, was arrested on suspicion of murder and is being questioned by Essex Police. He has been named locally as Mo Robinson from Portadown.
Police on Wednesday searched two addresses in Northern Ireland.
It is believed the lorry was refrigerated and had entered Essex through the Port of Tilbury after leaving the Belgian port of Zeebrugge.
Shaun Sawyer, the Chief Constable of Devon and Cornwall Police and the National Police Chiefs Council lead for modern slavery and human trafficking, said the incident was a tragedy that law enforcement, NGOs, the church and faith groups are working "every single moment of every single day" to prevent.
"So how many have we prevented? How many lives that we saved? Turn it on its head.
"It will be hundreds and thousands. But sadly, tragically, for 39 people that didn't work yesterday," he told BBC Radio 4's Today programme.
Mr Sawyer said: "You can't turn the United Kingdom into a fortress."
He said even if there were routes that were perceived as easier to get through, organised criminals would still exploit people who do not access those routes.
"The vulnerable, the women, the children, the non-English speakers - that happened in places like Syria who are exploited," he said.
"So that's a matter of policy for government about ease of access and routes, but conversely, all the time that we see people as commodity, and organised crime sees people as commodity, they will abuse any system, anywhere, any time, and that's what this is about... people as commodity and purveyors of hope actually dealing in despair."
Eric Van Duyse, a spokesman for the Belgian federal prosecutor's office, said that Brussels had started an investigation into the incident.
He added: "We have no idea at the moment how long the lorry spent in Belgium, it could be hours or days, we just don't know."
The deaths follow warnings from the National Crime Agency (NCA) and the Border Force of the increased risk of people-smuggling via Belgium and into quieter ports such as Purfleet.
The NCA previously said it had a "greater focus" on rising smuggler numbers in Belgium after the closure of a migrant camp, and a Border Force assessment highlighted Zeebrugge as being among "key ports of embarkation for clandestine arrivals".
The NCA has also warned that criminal networks are suspected to have started targeting quieter ports on the east and south coasts of the UK as well as the main Channel crossing between Calais and Dover.
Speaking on Wednesday afternoon, Deputy Chief Constable Pippa Mills said the lorry and the container were being moved to nearby Tilbury Docks so the bodies can be recovered while preserving the dignity of the victims.
"We are yet to identify them and must manage this sensitively with their families," she added.
Police have said tracking route used "will be a key line of inquiry".