Two small boats with a total of 36 migrants on board were intercepted while crossing the English Channel on Saturday.
It comes as the Home Office said French authorities had stopped 27 people from attempting to make the crossing since Friday evening.
A further 107 have been prevented from making the journey on small boats since last Sunday.
A least 8,400 people made the crossing in 2020, compared to 1,844 in 2019.
On 9 January, Border Force dealt with 103 people on six boats, while the French authorities stopped three vessels from entering UK waters.
One boat, with about 30 people on board, was rescued 23 miles off Beachy Head after it got "into difficulty".
Another 57 people in four boats were dealt with by the UK on Sunday, the Home Office said.