The 34 people found in a shipping container in Tilbury docks on Saturday are now in the process of claiming asylum in the UK.
The Homes Office said the men, women and children, aged from one to 72, were now in their care while their cases are being considered.
In a statement a Home Office spokesman said: "Following the conclusion of police interviews, the individuals involved have now been passed into our care.
"All 34 are now in the process of claiming asylum in the UK and we are providing accommodation and support to those who require it while their cases are considered.
"This tragic incident is a reminder of the devastating human consequences of illegal migration and we will do all we can to help bring those responsible to justice.
“The UK takes its international obligations extremely seriously and has a proud history of offering protection to those who need it. ”
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