The victims were discovered in a container on the back of a truck in Grays, east of London, on Wednesday, shortly after arriving by ferry from Belgium.
The local Essex Police force, which is working with immigration officials, said their initial priority was to try to identify the 39 victims.
The truck was moved Wednesday to a more secure location at nearby Tilbury docks so the bodies could be removed.
British media cited unidentified sources as saying on Thursday that the victims, thought to be 38 adults and one teenager, were Chinese nationals.
“The staff of the Chinese embassy in the UK is driving to the scene to verify this situation,” the Chinese foreign ministry said on its Weibo social media account.
“We read with a heavy heart the reports about the death of 39 people in Essex, England,” said an unverified Twitter account regularly attributed to China’s UK ambassador, Liu Xiaoming.
“We are in close contact with the British police to seek clarification and confirmation of the relevant reports,” it said.
The shocking discovery comes almost two decades after the bodies of 58 Chinese people were discovered in a Dutch truck at the southeastern English port of Dover. Two others survived.
In 2013, Spanish and French police dismantled a human trafficking ring that smuggled Chinese migrants into Europe and the United States, charging up to 50,000 euros per person.
The smugglers provided false identities and transport to take Chinese citizens to the United States and countries such as Britain, Spain, France, Greece, Italy, Ireland and Turkey, police said at the time.