A pregnant woman was among more than 40 migrants rescued during operations on both sides of the Channel.
One boat was intercepted off the coast of Kent, while French authorities picked up two others that had got into trouble.
A dinghy carrying 11 people, who were all said to be Iranian, was met by a Border Force cutter.
The expectant mother was among 20 people rescued from a boat that was taking on water near Dunkirk.
Eleven others, including two young children, were picked up off the coast of Calais after their engine failed.
All 31 rescued by the French were taken to Calais, where they were met by medics and border police.
The 11 people brought to the UK will now be interviewed by immigration officials, the Home Office said.
On Boxing Day, 49 people crossed the Channel in small boats, with 14 others returned to France.
The Home Office was accused of "criminalising refugees" after saying it would seek to return anyone who arrived in the UK illegally back to mainland Europe.
More than 1,800 have reached British shores after attempting to cross the Channel in small boats this year, according to BBC research.
In the same time, more than 120 people who arrived in small boats have been sent back to European countries, the Home Office said.
The Home Office said it would "always ensure we have the right resources in place to keep our border secure," adding: "Individuals who reach the UK illegally should be in no doubt about our determination to return them to Europe."