Twenty people, including 18 Albanians, were rescued from the English Channel in the early hours of Sunday after the inflatable boat they were in started taking on water.
The two other people on the boat are British, the Home Office has confirmed.
Among those rescued from rigid-hulled inflatable boat were a woman and two children, the Home Office said.
All were taken to Dover and where they were questioned by Border Force officers.
- Video report by ITV News correspondent Sally Lockwood
The UK Coastguard received a call for assistance just off the coast of Dymchurch in Kent, at 11.40pm on Saturday, and the boat was found at 2am.
It has been reported the people on board the boat alerted their families in Calais when they came into trouble, and they raised the alarm with the French authorities.
A search and rescue helicopter was deployed as well as lifeboats from Dungeness and Littlestone as part of the operation, as well as coastguard rescue teams from Dungeness and Folkestone.
A separate vessel was also discovered on the beach at Dymchurch.
It is not known at this stage if that boat is linked to the other vessel, but it has been seized by law enforcement officials.
The incident has raised concerns over the security of the UK's coastal borders.
Councillor Mary Lawes, Ukip group leader on Shepway District Council, said: "We are not doing enough to control our coastline, the Government has to address border controls, something has to be done to protect these people from harm and our borders."
But David Monk, Conservative leader of the local authority, said he believed high levels of surveillance in the English Channel would mean most boats crossing the channel would be identified.