A witness said a group of up to 38 migrants were caught attempting to travel across the Channel to Kent shortly before midday on Tuesday.
A lone man was also picked up separately by French authorities near Calais while reportedly swimming with a rubber ring and flippers, according to the BBC.
Speaking about the man who was detained near Calais, former coastguard Andy Roberts said: "I've seen every kind of attempted unorthodox crossing of the Dover Strait.
"This one is absolutely incredible. Anyone who thinks with a rubber ring and some flippers they can swim 21 miles as the crow flies... is really asking for serious trouble."
Pictures in Dover showed a woman carrying a young child as UK Home Office officials processed the group.
Another photograph appeared to show some of the people wearing orange life jackets as they were taken to shore in a Border Force rigid-inflatable boat.
A boat which appears to have been used by the migrants during their crossing was also being tugged.
A spokesman for the Home Office said Border Force was "dealing with three ongoing small boat incidents off the Kent and Sussex coasts".
HM Coastguard also confirmed it helped Border Force with three incidents.
A spokesman added: "We are only concerned with preservation of life, rescuing those in trouble and bringing them safely back to shore, where they will be handed over to the relevant partner emergency services or authorities."