More than 120 migrants have arrived in England after attempting to cross the Channel so far this weekend.
On Saturday, Border Force dealt with 103 people on six boats, while the French authorities stopped three vessels from entering UK waters.
Another 20 people in two incidents have been dealt with by the UK so far on Sunday, the Home Office confirmed.
Border Force is currently dealing with an ongoing small boat incident, it added.
The coastguard’s fixed-wing aircraft and Border Force vessels Searcher, Vigilant and Neptune have been searching UK waters.
One boat, with about 30 people on board was rescued about 23 miles off Beachy Head after it got “into difficulty” on Saturday.
The government said it would assess each person and look to return those who have no legal right to remain.
Minister for Immigration Compliance Chris Philp said: “Legislative changes to the law are being made to enable cases to be treated as inadmissible if they have travelled through a safe country.”
The number of migrants reaching the UK by boat was four times greater in 2020 than 2019, official figures have shown.
At least 8,400 people made the crossing in 2020 while the year before, 1,844 did.