Seventy-four people including children have been detained after eight small boats were intercepted in the English Channel.
The vessels were intercepted by Border Force officials off the UK coast on Saturday.
Home Secretary Sajid Javid called the situation "deeply concerning", while Conservative MP for Dover and Deal, Charlie Elphicke, said it was "a record number of boats in a single day".
Mr Javid said: "The number of migrants crossing the Channel overnight is deeply concerning and I'm receiving regular updates on the situation.
"Those who choose to make this dangerous journey across one of the busiest shipping lanes in the world are putting their lives in grave danger - and I will continue to do all I can to stop them."
He said the UK Border Force had stepped up its activity out of the Joint Co-ordination and Information Centre in Calais.
Mr Javid added: "It is an established principle that those in need of protection should claim asylum in the first safe country they reach, and since January more than 30 people who arrived illegally in the UK in small boats have been returned to Europe.
"We will continue to seek to return anyone who has entered the UK illegally."
Only one of the eight vessels made it to shore, landing at Winchelsea Caravan Park beach, East Sussex.
Two other vessels were stopped by the authorities in France.
The Home Office said all those detained have been assessed and cleared by medical staff and were now being processed by immigration officials.
It added that the nationalities of the detainees were still being determined, and a criminal investigation has been launched.
HM Coastguard initially said it had assisted Border Force colleagues with 13 vessels, but it said the higher figure was due to multiple reporting as events unfolded.
Images of men being given blankets by emergency service workers on Winchelsea beach were shared on Twitter.
A spokesman for Kent Police said it had provided support to the Border Force.
