“Multiple” migrant boats have been picked up by Border Force in the English Channel, the coastguard said.
One vessel is believed to have landed on a Kent beach, with pictures showing a group being detained in Dungeness.
French authorities said they rescued 58 people from three boats, one of which had 30 migrants on board, including six children and two people with physical difficulties.
A record 202 people in 20 vessels reached the UK on Thursday.
The Home Office has been contacted for comment.
Two Border Force vessels were deployed, alongside an RNLI lifeboat and coastguard rescue teams, during the latest operation.
About 3,400 people have reached the UK in small boats this year, with more than 1,000 arriving in July alone.
Home Office minister Chris Philp MP said on Thursday the number of crossings was “unacceptably high”.
French authorities have stopped thousands of migrants this year, “but more needs to be done,” he said.
“We need stronger enforcement measures, including interceptions at sea and direct return of boats and the French have heard that directly from the home secretary,” he said.
A boat carrying five people was rescued by a French coastguard vessel at about 19:30 on Thursday after getting into difficulty off the coast of Calais.