Five lifeboats and four Border Force vessels escorted groups to Dover as a period of calm and mild weather made the journey less risky.
A Whitehall source accused France of losing control of the situation.
The Home Office said British people did not want to see people die in the Channel as ruthless gangs profit.
More than 23,000 people have made the crossing from France to the UK by boat so far this year, a sharp rise on the 8,404 in 2020 – and far more than in years before the pandemic, when most asylum seekers arrived by plane, ferry or train.
About 98% of people who arrive in the UK via the Channel apply for asylum.
But overall applications for asylum fell in the months after global travel was limited due to Covid-19, and numbers remain slightly lower than before the pandemic.
In 2019, there were 35,737 asylum applications, which fell to 29,815 in 2020.
Figures for the first half of 2021 showed 14,670 applications.
In recent years, asylum applications in the UK peaked during the European migration crisis of 2015-16.
UK officials say they want to stop the Channel crossings – describing them as dangerous and unnecessary.
A Home Office spokesperson said the number of migrant crossings on Thursday was “unacceptable”.
The previous record was 853 people crossing on 3 November.
“The British public have had enough of seeing people die in the Channel while ruthless criminal gangs profit from their misery and our New Plan for Immigration will fix the broken system which encourages migrants to make this lethal journey,” the spokesperson said.
Migrants crossing Channel to UK hits new daily record