A 25-year-old driver, from Northern Ireland, has been arrested on suspicion of murder.
The victims, found at the Waterglade industrial park in Grays, included one teenager and the remaining were adults, Essex police said.
The force said the lorry is believed to be from Bulgaria but entered the country in Holyhead, the Welsh port town that serves Ireland.
The home secretary, Priti Patel, said Home Office immigration officials were working closely with the police to establish what happened.
Police officers were called by the ambulance service shortly before 1.40am on Wednesday following the discovery of a container with people inside at the industrial park in Eastern Avenue.
Ch Supt Andrew Mariner said: “This is a tragic incident where a large number of people have lost their lives. Our inquiries are ongoing to establish what has happened.
“We are in the process of identifying the victims. However I anticipate that this could be a lengthy process.
“We believe the lorry is from Bulgaria and entered the country at Holyhead on Saturday 19 October and we are working closely with our partners to investigate.
“We have arrested the lorry driver in connection with the incident who remains in police custody as our inquiries continue. I appreciate this cordon is going to disrupt the activity of local businesses in the area and we will work to ensure that disruption is kept as short as possible.
“We are working with Thurrock council to mitigate against any impact our investigation scene will have locally.”
The prime minister, Boris Johnson, said he was “appalled by this tragic incident in Essex”.
“I am receiving regular updates and the Home Office will work closely with Essex police as we establish exactly what has happened,” he wrote on Twitter.
Patel said: “I’m shocked and saddened by this utterly tragic incident in Grays. My heart goes out to all those affected.
“Essex police has arrested an individual and we must give them the space to conduct their investigations. Home Office immigration officials will be working closely alongside them to establish how this horrific event came to happen.”
Richard Burnett, the chief executive of the Road Haulage Association, said: “This tragedy highlights the danger of migrant gangs people-smuggling on lorries.”
He added: “It’s highly unlikely that if this vehicle has come from Europe that it’s been physically checked. Because of the migrant issue at Dover and Calais, you’ve got far more checks.”
Seamus Leheny, the Northern Ireland policy manager for the Freight Transport Association, said: “If the lorry came from Bulgaria, getting into Britain via Holyhead is an unorthodox route. People have been saying that security and checks have been increased at places like Dover and Calais, so it might be seen as an easier way to get in by going from Cherbourg or Roscoff, over to Rosslare, then up the road to Dublin.
“It’s a long way around and it’ll add an extra day to the journey.”
The discovery is not the worst of its kind in the UK. The bodies of 58 Chinese people were found in a container at Dover, Kent, in 2000.
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