More than 60 migrants have crossed the Channel in six boats.
Five vessels were intercepted by Border Force off the coast of Kent, with a sixth landing on a beach in Sussex.
The Home Office said 53 migrants - including what it called six "claimed minors" - found in the Channel would be interviewed by immigration officers.
A further 11 people, including four children, were detained by police and handed over to Border Force after arriving at Winchelsea Beach by boat.
Sussex Police said it was "very concerned" for another group, which it described as "possibly a family including children", who may have left the beach before authorities arrived.
Ch Insp Anita Turner said: "We want to make sure that these people are safely ashore and that they are okay."
Meanwhile, two dinghies carrying a total of 19 adults, 10 children and a baby were picked up by French authorities attempting to cross the Channel.
More than 900 people, including at least 80 children, have crossed the Channel in small boats this year.
The Home Office said it was monitoring the "ongoing situation" and "working closely at all levels with French authorities," adding Home Secretary Priti Patel was due to "raise this issue with her French counterpart in the coming days".
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
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