Nearly 2,000 migrants arrived in the UK in the last week - the highest weekly total in 2021 so far.
A total of 1,959 people crossed the English Channel from France in the week to September 10, data shows.
And in the seven days to September 12, the most recent seven-day period, 1,876 people crossed to the UK.
At least 14,400 people have crossed to the UK on small boats this year.
The total for 2021 so far is just over 6,000 higher than the number of people who crossed to the UK in 2020.
It comes as more migrants arrived in Kent on Monday as the weather cooled and as the south coast saw breezy but clear conditions at sea.
Several young children were among a group seen arriving in Dungeness, Kent, while immigration officers were seen taking care of a woman who was ill after she was brought ashore on a stretcher by police and Royal National Lifeboat Institution (RNLI) members.
Mr Darmanin said France would not accept any practices which breach maritime laws, or be subjected to financial blackmail – referring to suggestions from Ms Patel that she could withhold millions of pounds of cash meant to help step up patrols unless an improvement in the number of migrants intercepted by French authorities is seen.
The so-called turnback tactics has been slammed by aid charities and campaigners who fear migrants lives could be at risk.
The legality of the tactic was also called into question, but ministers insisted the UK would not infringe international law.
Border Force staff are understood to have been given special training on handling migrant boats, with the decision on how to approach an incident down to individual captains.
The turnback tactic could reportedly involve officers on high-powered, armoured jet skis physically turning small boats around and escorting them back to France.