Three boats with 35 migrants on board were intercepted by Border Force officers on Sunday.
The first boat was spotted at about 03:35 BST with 10 men and three women onboard, all saying there were Iraqi or Iranian, the Home Office said.
Thirteen men, who presented themselves as Syrian, Yemeni, Iraqi and Palestinian were picked up at 06:55.
The third boat with nine migrants onboard was intercepted at about 13:15, a Home Office spokesperson said.
All were brought to Dover for medical assessments.
More than 50 migrants were prevented from leaving the French shore on Sunday, or picked up in the Channel and returned to France, the country's authorities said.
'Left a safe country'
The Home Office said 79 men and 11 women had crossed the Channel on Saturday 16 May on six small boats.
Chris Philp, minister for immigration compliance, said: "Criminal intelligence continues to be shared between the NCA and French authorities.
"The migrants have left a safe country and we are seeking to return specific cases where appropriate."
Roger Gough, the leader of Kent County Council, said the number of young asylum seekers in the county had "doubled in a little more than a year".
He said a reduction in the numbers of lorries crossing the Channel due to coronavirus had led to a rise in the number of children crossing in small boats.
Some 20 children arrived in small boats over the bank holiday weekend, he added.