The National Crime Agency said investigators were questioning two men from Sudan, aged 19 and 22, and a third 22-year-old suspect from South Sudan over the tragedy.
They were arrested on suspicion of facilitating illegal immigration and of entering the UK illegally themselves.
The 55 surviving boat passengers have been interviewed and are expected to be spoken to again in the coming days.
Craig Turner, NCA deputy director of investigations, said: "This tragic incident once again demonstrates the threat to life posed by these crossings and brings into focus why it is so important to target the criminal gangs involved in organising them.
"We will do all we can with partners in the UK and France to secure evidence, identify those responsible for this event, and bring them to justice." More than 400 migrants arrived in the UK on Tuesday, the day the group of five died.
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