Nine boats carrying 125 migrants have been intercepted on their way to the UK as searches continue for more vessels.
The Home Office said Border Force dealt with several incidents on Friday after being alerted to small boats in the Channel.
Meanwhile, French authorities picked up three migrants in a kayak plus another 15 in a broken down boat and returned them to France.
No nationality details were available at this stage, the Home Office said.
The migrants would be interviewed and dealt with in line with immigration rules, transferring to detention where appropriate, it added.
The first boat was intercepted at about 00:30 BST on Friday and 14 men were found on board.
Vessels continued to arrive throughout the night and well into the next day, each with between eight and 19 people on board.
The coastguard said it had also been dealing with several incidents on Saturday morning and was coordinating a search and rescue response.
More than 2,800 migrants have reached the UK this year, with a record number of 180 arriving on Sunday alone.
Minister for Immigration Compliance and the Courts Chris Philp said: “It is in the interests of both France and the UK to stop people making this dangerous journey.
“The French have prevented more than 200 attempts in the past week alone, but more action is required.”
He said a new Franco-British intelligence cell would “go after the criminals facilitating these crossings” and stronger enforcement measures were being explored.
On Friday, Calais MP Pierre-Henri Dumont accused the British Home Secretary of fake news by suggesting the French were not stopping boats from making the crossing.
Priti Patel told the Commons Home Affairs Committee the British and French governments disagreed on whether it would be lawful to intercept boats.
Mr Dumont said: “It’s not true to say we are doing nothing, it’s quite the opposite actually.”