Staff at Tilbury Docks near London discovered one dead man in his 40s, and 34 other people alive, after hearing banging and screaming from inside the container yesterday.
British police said the survivors, including 13 children, were Afghan Sikhs.
"I didn't know of this until the news reports emerged and I am trying to contact families who may be involved," Rawel Singh, a prominent leader of Afghanistan's Sikh community, told AFP.
Singh, vice president of the Hindu and Sikh Council of Afghanistan, said only a few thousand Sikhs remained in Afghanistan, a sharp drop from before the civil war in the 1990s.
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Many of those remaining complain of brutal persecution in a Muslim-majority country that has been ravaged by decades of war.
"Our rights are trampled and we are treated badly by the Afghan people," Singh said.
"We are discriminated against, our children cannot attend school, and our land has been stolen. Therefore many Sikhs are forced to flee Afghanistan."
Afghan's Sikhs and Hindus often live in the same communities in Kabul, Jalalabad and Kandahar, working as labourers or in the clothes and traditional medicine businesses, said Singh.
All 34 survivors from the shipping container were taken to nearby hospitals to be treated for hypothermia and dehydration.
Four people are still in hospital, and the local Sikh community has been helping care for the survivors.
"Officers and colleagues from the Border Force will be speaking to them via interpreters so we can piece together what happened," said superintendent Trevor Roe of the local Essex police.