Adults carrying youngsters and others wrapped in blankets were seen arriving on the south-east coast of England on Saturday with help from lifeboat crews.
Official figures have not been confirmed but it is believed hundreds of people made the journey.
Meanwhile, French officials said 243 people in difficulty were recovered and brought to safety at the ports of Boulogne-sur-Mer, Dunkirk and Calais.
More than 24,700 people have arrived in the UK so far this year after making the Channel crossing in small boats – almost three times the number there were in 2020.
This includes at least 1,247 who arrived since Monday, according to data compiled by the PA news agency. This number is set to rise as the exact figure for Tuesday is still being finalised by the Home Office.
It is thought at least 10 migrants have died in the last few weeks while trying to make the dangerous crossing.
The arrivals came as it was reported asylum seekers will have to obey strict rules in new centres or face their claims being rejected under plans advocated by Home Secretary Priti Patel.
Kevin Saunders, former chief immigration officer for the UK Border Force, argued that people who arrive in the UK via the Channel need to be processed offshore.
He told Times Radio: “The most effective way would be to take all the people who have arrived in the UK to an offshore processing centre and deal with it offshore.
“That is the only way you will stop people from coming into the UK. We’ve seen trying to do it with the French on land, on the Channel, nothing works.”
Asked why it had to be offshore, he said: “People will still come to the UK, because they know we are not going to be able to remove them from the United Kingdom when their asylum claim fails.”
He said only a small number of people had been removed this year and described the UK as “just too attractive” for people, adding: “They know that once they’re in the UK they’ve won the jackpot.”
The Home Secretary has been impressed with centres being built in Greece where migrants were put under strict curfews and faced routine checks on their movements, the Daily Telegraph reported.
A UK government source was quoted by the Telegraph saying if migrants breached new rules, their asylum claim could be impacted.
Meanwhile, the Times reported that Boris Johnson had drafted in Chancellor of the Duchy of Lancaster Steve Barclay to oversee the issue of the rising number of migrants arriving on Britain’s shores.
The newspaper said that the PM was “exasperated” with the situation following a number of strategies to stem the flow.
The move to bring in Mr Barclay could be seen as an admission that Ms Patel has not managed to tackle the issue.
It comes after Sir Keir Starmer accused her of failing to deliver on promises to stem the flow of illegal migrants crossing the Channel.
The Labour leader said she had not secured strong enough agreements with the French government to prevent migrants making the dangerous sea journey.
He said the Home Secretary repeatedly used “strong language” to say how she would tackle the problem, but delivered “absolutely nothing”.