Four small boats carrying 87 people including children made the dangerous Channel crossing into the UK on Saturday.
The Home Office has said all adults who arrived in Dover were tested for Covid-19, and one person tested positive.
The department could not confirm the nationalities or ages of those involved.
French authorities also prevented two attempted crossings involving a further 51 people on Saturday.
Following the incident, the Home Office said: “People should claim asylum in the first safe country they reach and not risk their lives making these dangerous crossings.
“We are continuing to pursue the criminals behind these illegal crossings.
“Police patrols on French beaches and enhanced intelligence sharing between our security and law enforcement agencies has helped to prevent crossings.
“The Government is also returning illegal migrants who have no right to stay in the UK to safe countries.
“In January, new rules were introduced which make asylum claims inadmissible where people have travelled through safe countries to get to the UK through illegal routes.”