Seventy-four people including several children have been detained after eight small boats tried to cross the Channel.
Home Secretary Sajid Javid described the incident as “concerning”, after the vessels were intercepted by Border Force officials off the UK coast on Saturday.
Only one of the eight vessels made it to shore, landing at Winchelsea Caravan Park beach, East Sussex.
Two other vessels were stopped in France by the authorities there.
All those detained have been assessed and cleared by medical staff and are now being processed by immigration officials, the Home Office said.
It said the nationalities of the detainees are still being determined, and a criminal investigation has been launched.
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.”
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.
Border Force vessels, RNLI lifeboats from Dover, Dungeness and Rye and coastguard rescue teams from Folkestone, Langdon and Rye Bay were involved in the response.
Images of men being given blankets by emergency service workers on Winchelsea beach have been shared on Twitter.
A spokesman for Kent Police said it had provided support to the Border Force.
Kent MP Charlie Elphicke claimed the events would mean “a record number of boats arriving in a single day”.
He added on Twitter: “This crisis was meant to have been dealt with at Christmas, yet numbers continue to rise.
“It looks set to surge to record levels through the summer.
“The Home Office needs to get a grip on this crisis.”