Tensions with France already strained amid Brexit rows over fishing and Northern Ireland, have escalated in recent days after 1,185 people reached the UK in a single day last week.
French interior minister Gerald Darmanin has blamed Britain’s work market for enticing people to make the perilous crossing.
Meanwhile, young children were seen being carried ashore in Dover on Monday after more people risked death crossing the English Channel.
A toddler wrapped in a light blue hoodie looked around at border officials as he was carried in the arms of a woman.
The pair, possibly mother and child, were closely followed by an older child and a man after they and others were brought into the Kent port aboard a Border Force patrol boat.
The new arrivals came amid reports that a jet-ski used to cross the Channel has been recovered at sea by the RNLI and towed ashore in Dungeness.
More than 23,500 people have now reached the UK after crossing the English Channel on board small boats this year, according to data compiled by the PA news agency.
More than 3,770 people succeeded in crossing to Britain in the first two weeks of November, PA data shows.
Home Secretary Priti Patel spoke to her French counterpart Mr Darmanin on Monday about the ongoing issue of Channel crossings.
In a joint statement, the pair said they had agreed to “to strengthen operational cooperation further” and “to accelerate the delivery” of commitments made when they spoke back in July.
Earlier, Mr Darmanin told French media that NGOs “preventing the gendarmerie from working” are largely British with British citizens working on French soil.
He added: “Smugglers organising networks and making large sums of money… exploiting women and children, who are often fragile and from Africa and the Middle East, are often in Great Britain.”
Downing Street says further action is needed to stem the flow of people crossing the Channel.
The Prime Minister’s official spokesman said Ms Patel is seeking talks with her French counterpart about what more can be done.
“It is clear that we need to keep working with our French counterparts to do more to prevent these crossings, which are putting lives at risk,” the spokesman said.
“We continue to see France as a close ally of the UK.
“We do want to work constructively to resolve this issue
“We are providing funding to the French to allow them to increase surveillance, to allow them to increase the police presence that it there to prevent these crossings taking place.
“Through that investment we have seen stoppages increase and that is to be welcomed but clearly with the level crossings we are seeing per day more needs to be done.”
On a grey morning in Dover, dozens of people were seen being brought ashore aboard Border Force’s patrol boat Hurricane.
While many were men, border officials were also seen ushering at least six children up the gangway.
Two children and a woman were seen walking up to the quayside, accompanied by a border official who appeared to pat one of the youngsters on the back and reassure them.
Another child was seen being carried in the arms of an immigration officer as they were taken off the boat.
About 20 miles along the coast at Dungeness, lifeboat crews were seen towing a jet-ski on to the beach.
The RNLI is believed to have been tasked to an incident at sea earlier on Monday morning, leading to suspicions that the jet-ski was used in a Channel crossing.
The coastguard confirmed that it had been co-ordinating a search and rescue response to an incident off Kent and had sent the coastguard helicopter a lifeboat.
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