British police said 39 bodies were found near London on Wednesday in the container of a truck thought to have come from Bulgaria.
Essex Police said the people were all pronounced dead at the scene in an industrial park in Grays, east of London. Early indications suggest the victims are 38 adults and one teenager.
A 25-year-old man from Northern Ireland has been arrested on suspicion of murder.
"This is a tragic incident where a large number of people have lost their lives," Essex Police chief superintendent Andrew Mariner said in a statement.
British Prime Minister Boris Johnson said he was "appalled" and sent his sympathies to the victims' families.
"I'm appalled by this tragic incident in Essex," he said.
"I am receiving regular updates and the Home Office will work closely with Essex Police as we establish exactly what has happened.
"My thoughts are with all those who lost their lives and their loved ones."
The police said they were alerted by the ambulance service shortly before 1:40am (0040 GMT) following the discovery of a truck container with people inside at the Waterglade Industrial Park.
"We are in the process of identifying the victims. However I anticipate that this could be a lengthy process," said Mariner.
"We believe the lorry is from Bulgaria," said Mariner.
"We have arrested the lorry driver in connection with the incident who remains in police custody as our enquiries continue."
He said it was thought the truck entered Britain on Saturday at Holyhead on the northwest tip of Wales -- one of the main ports for ferries from Ireland.
The UK and the Republic of Ireland are not in the European Union's no-borders Schengen zone but have their own historic Common Travel Area, meaning there are no checks on the movement of goods or people between the two.
Richard Burnett, chief executive of the Road Haulage Association which represents truck drivers in Britain, said: "Our thoughts are with the families of the deceased but whatever the circumstances, it highlights the danger of migrant gangs people-smuggling on lorries."
Jackie Doyle-Price, the MP representing the local Thurrock constituency surrounding Grays, said the news was "sickening".
"People trafficking is a vile and dangerous business," she said.
"Let's hope they bring these murderers to justice."
Home Secretary Priti Patel, Britain's interior minister who represents an Essex constituency, said she was "shocked and saddened by this utterly tragic incident.
"Essex Police has arrested an individual and we must give them the space to conduct their investigations."
Cases of this kind are rare in Britain.
In 2014, staff at the Tilbury container port -- next to Grays -- heard screaming and banging coming from inside a shipping container, and found 34 Afghan Sikhs alive inside suffering from severe dehydration, hypothermia and lack of air.
One man was found dead, having passed away during the sea crossing from Belgium.