A homicide investigation is continuing into the death of one of the 35 rescued yesterday at Tilbury Docks in Essex from Belgium.
They were treated for severe dehydration and hypothermia before being taken to a detention centre.
They are being held under UK immigration laws and it is expected they will be interviewed through interpreters at the immigration centre near Tilbury.
Essex Police described the men, women and children as victims of "people trafficking" and are working with Interpol and other international authorities to try to establish what happened.
One man is believed to have been questioned by officers already and most of the others have been discharged from hospital.
The Indian Ministry of External Affairs (MEA) has confirmed contacting UK authorities but stressed that the nationality of the survivors was yet to be established.
Some media reports here had indicated that the group belonged to the Punjab region.
The discovery was made after the container arrived from the Belgian village of Zeebrugge early on Saturday morning when "screaming and banging" were heard coming from inside.
Belgian police said they believed the lorry which delivered the container in Zeebrugge had been identified through CCTV footage.
Chief Inspector Peter De Waele, from the Belgian police, said: "The Belgian civil police is checking all the images and my colleagues are very, very hopeful that we find the truck who put the container in Zeebrugge.
It is not known where the container, one of 64 aboard the P&O commercial vessel Norstream, originated, nor where the people inside it were heading.
"It shows how desperate people are to improve their economic situation - how desperate they are to leave their own homes, and own countries, and hope to arrive in somewhere that's more accommodating, more kind, and offering them a better quality of life. Usually, they're sadly wrong," said Anthony Steen, chairman of the UK's Human Trafficking Foundation.
