Police believe those arrested charged people thousands of pounds to bring them to the UK illegally.
Four Vietnamese nationals accused of advertising their people smuggling services on Facebook have been arrested in England.
Officers arrested a 23-year-old woman in Croydon, south London, a 64-year-old man in Deptford, south London and a 34-year-old man in Leicester on Monday on suspicion of assisting unlawful immigration.
A 25-year-old man was arrested at the same property in Croydon after he was allegedly involved in people smuggling and drug offences.
In Paris, 12 people have also been arrested as part of the investigation into the group accused of sharing posts aimed at the Vietnamese community, advertising illegal crossings and charging those willing to make the trip thousands of pounds.
The older man arrested in London is thought to have acted as a driver, collecting migrants who arrived on small boats and on at least one occasion bringing them back to the Croydon address, the National Crime Agency (NCA) said.
He will now face extradition proceedings while the others were charged and appeared at Croydon Magistrates Court on Tuesday, they added.
According to the government, an increasing number of migrants arriving illegally in the UK via the Channel are from Vietnam.
Home Secretary James Cleverly said: “We are using every possible lever at our disposal to crack down on people smugglers and break their supply chains.
“Just last week, we signed a new agreement with Vietnam, strengthening our cooperation on illegal migration.
“Together with law enforcement agencies such as the NCA, our French partners, and other countries like Vietnam, we are committed to dismantling the criminal gangs who are trying to turn a profit by abusing our borders.”
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Chris Farrimond, NCA director of threat leadership, said: “Vietnamese nationals now make up a large number of those we see arriving on small boats.”
He added: “We allege this group were advertising their crossing services on social media to encourage others from their country to make the same treacherous journey.
“The NCA is continuing our work with partners and has had thousands of social media pages and posts advertising organised immigration crime services removed from platforms.”
Mr Farrimond added: “Tackling organised immigration crime is a priority for the National Crime Agency and our investigation continues to target people smugglers both in the UK and overseas at every step of the route.”
