A pregnant woman was among more than 40 migrants rescued during three operations on the English and French sides of the Channel.
One boat carrying 11 people claiming to be from Iran was intercepted by UK emergency services off the coast of Kent and brought to Dover on Sunday morning.
Meanwhile, French authorities picked up two other small vessels that were in trouble in the early hours of the day.
The expectant mother was among 20 people rescued from a boat that was taking on water near Dunkirk. A second rescue involved 11 people on board a boat off Calais.
On Boxing Day, 49 people crossed the Channel in small boats, with 14 others returned to France.
The incidents come amid suggestions the number of people prepared to risk the crossing has increased over the past year.
Research suggests more than 1,800 have reached British shores after attempting to cross the Channel in small boats this year.
This is in contrast to figures published by the Home Affairs Select Committee showing 562 people were recorded as attempting to cross last year, with 297 making it to the UK.
A Home Office spokesman said: “Illegal migration is a criminal activity.
“Those who seek to come to the UK unlawfully and the ruthless criminals who facilitate journeys are all breaking the law and endangering lives.
“We will always ensure we have the right resources in place to keep our border secure.”
He added: “Individuals who reach the UK illegally should be in no doubt about our determination to return them to Europe as it is an established principle that those in need of protection should claim asylum in the first safe country they reach.”
A 42-metre Border Force cutter and two coastal patrol vessels will be keeping watch in the Channel over the Christmas and New Year period.
Drones and specialist vehicles have also been deployed to stop small boats leaving French shores and arriving in the UK illegally.