The UK Border Force has been dealing with several boats that have crossed the English Channel carrying migrants.
HM Coastguard said it had assisted with nine vessels off the Kent coast. Earlier, it was reported four boats with 30 people had been intercepted.
Eight men with an inflatable dinghy were also spotted on Winchelsea Beach, in East Sussex.
The Conservative MP for Dover and Deal, Charlie Elphicke, said it was “a record number of boats in a single day”.
He tweeted: “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.”
Mr Elphicke said he would be meeting the home secretary on Sunday.
The Marine and Coastguard Agency said RNLI lifeboats from Dover, Dungeness and Rye had been involved in the incidents, along with coastguard rescue teams from Folkestone, Langdon and Rye Bay.
It earlier reported a higher figure of 13 “incidents” but this was downgraded due to multiple reporting as events unfolded.
Last month, 140 migrants were picked up – the highest number since December, when a “major incident” was declared.