Mark Stribling, 35, from Farningham, Kent, and Robert Stilwell, 33, from Dartford, appeared at Medway Magistrates’ Court to face charges under Section 25 (1) of the Immigration Act 1971.
They were ordered to remain in custody until the next hearing, at Maidstone Crown Court on June 27.
Two children and a woman were among the group of 18 Albanians aboard the rigid-hulled inflatable boat which began to sink off Dymchurch, Kent, on Saturday night.
Along with the Albanians, two British men were also rescued by the Coastguard, working with the RNLI, and handed over to the Border Force.
It has been reported the people on board had alerted their families in Calais, who raised the alarm with the French authorities.
A second vessel, believed to be linked to the inflatable that got into trouble, was discovered on the beach on Sunday at Dymchurch and was seized by the authorities.
The incident has sparked fears that tragedies seen in Greece or Italy could start to occur in the Channel.
President of the French coastguard, Bernard Barron, told Sky News: “It’s starting to become a very similar situation to that seen in the Mediterranean and my biggest fear is that the same kind of tragedies we see in Greece or Italy will start to repeat in the Channel.”
Mr Barron said that, even though the smugglers are being given large sums of money, there are not providing suitable transport for a “sea filled with danger, with strong currents, storms and heavy traffic of larger vessels”.
Lucy Moreton, general secretary of the Immigration Services Union, said large stretches of Britain’s coastline is being left unpoliced and officials simply do not know how many people have sneaked into the country undetected.
However, she said her “gut feeling” and anecdotal evidence suggest Britain’s coasts are facing the biggest ever onslaught of people smugglers.
The incident came after 17 suspected Albanian migrants and a British man wanted on suspicion of murder in Spain were detained after a catamaran arrived at Chichester Marina in West Sussex on Tuesday last week.
The 55-year-old man, who was the subject of a European Arrest Warrant, was also detained on suspicion of facilitating illegal immigration, while the 17 Albanian men were held on suspicion of entering the UK illegally.
The Albanians in this earlier incident have been detained pending Home Office consideration of their cases.
Last month, two Iranian men were found floating in an ill-equipped dinghy in the English Channel.