Essex Police have launched a murder investigation this morning (Wednesday) after the discovery was made inside a lorry container on an industrial estate in Grays.
Among the victims included the body of a teenager, the force confirmed.
A 25-year-old man from Northern Ireland has been arrested on suspicion of murder.
Officers were called by the ambulance service shortly before 1.40am on Wednesday following the discovery of a lorry container with people inside at Waterglade Industrial Park, Eastern Avenue, Grays.
Some 38 adults and a teenager were pronounced dead at the scene. Enquiries are now underway to identify them.
Chief Superintendent Andrew Mariner said: "This is a tragic incident where a large number of people have lost their lives. Our enquiries 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 enquiries 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 lorry is from Bulgaria and entered the UK at Holyhead in north Wales, one of the main ports for ferries from Ireland.
Prime Minister Boris Johnson said he was "appalled by this tragic incident", adding: "My thoughts are with all those who lost their lives and loved ones."
Road Haulage Association chief executive Richard Burnett said the lorry could have travelled on a ferry from Cherbourg, France, to Rosslare, Ireland, before driving to Dublin and taking another ferry to Holyhead, North Wales and then reaching Kent by road
He told PA: "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 that are taking place there. You've got heartbeat monitors, you've got dogs, you've got CO2. Those checks are done as you drive through.
"Cherbourg, because it's a low volume port, you probably won't have the same security measures that they have in Coquelles, Calais, for the high number of vehicles that are stepping through there and that's been one of the main migrant routes historically.
"If this is somebody trying to smuggle a significant number of people through then maybe Cherbourg has been picked because it's a little easier to get through."
The National Crime Agency (NCA) said: "We are aware of this tragic incident which is now the subject of a murder investigation being led by Essex Police and we have deployed NCA officers to assist.
"We are working with partners including Essex Police and Immigration Enforcement to provide specialist support to urgently identify and take action against any organised crime groups who might have played a role in causing these deaths."