Migrants were rescued from a second sinking boat on the same night four people died in the Channel.
Border Force officers rescued 50 people, five of whom had ended up in the freezing water, after their boat started to sink on the same night a major search and rescue operation was launched when a dinghy capsized, Government officials said.
Detectives from Kent Police are now investigating the circumstances surrounding the incident in the early hours of Wednesday morning.
Four people died and 39 others were rescued alongside the National Crime Agency (NCA), amid reports that those on board paid thousands of pounds to people smugglers to make the journey to the UK.
Officers are also trying to identify the people who died and track down their relatives, the force said on Friday.
The search was called off at 5pm on Thursday.
Migrants on board the dinghy told fishermen they had paid £5,000 each to people smugglers for the journey from France to the UK, according to media reports.
Earlier this week, Prime Minister Rishi Sunak announced more funding for the NCA – Britain’s version of the FBI – to tackle organised immigration crime in Europe.
NCA director-general Graeme Biggar said: “This incident, tragically, highlights the dangers of these crossings, a high percentage of which are facilitated by organised criminal networks.
“They treat people as a commodity to be profited from and think nothing of putting them in incredibly dangerous situations. Working with our partners on both sides of the Channel we are determined to find those responsible and bring them to justice.”
The NCA is also involved in the French probe into the deaths of at least 27 migrants in the Channel last year.