The French news channel BFM TV first reported the news, citing French police sources. A coastguard official said a rescue operation was still underway.
Three rescue vessels and one helicopter appeared to be attending the scene, according to information available on the MarineTraffic app.
“A search and rescue operation is under way off the coast of Calais…We think several people have died as their vessel sank,” a police source told Reuters on Wednesday afternoon.
The source did not give the exact number of people who had died, adding that doctors would have to confirm the death toll first.
Gerald Darmanin, the French interior minister, also confirmed there had been fatalities in the Channel after a boat capsized on Wednesday. Announcing the news on Twitter, he added that “we can never say enough about the criminal nature of the (people) smugglers”.
The latest fatalities follow a string of other migrant deaths in the Channel in recent weeks, amid a record number of people attempting the crossing. On 11 November, a total of 1,185 people arrived in England by boat, the most in a single day.
One man died making the dangerous crossing on 3 November, while another was found dead the following day on a beach near Calais, after French officials found a boat filled with water.
Late last month, another man lost his life after falling off a dinghy as he attempted to reach England. Home secretary Priti Patel confirmed his death to a House of Lords committee on 27 October.
“We want to stop people from drowning at sea, only yesterday there was a loss of life,” she told the group of peers.
However, despite these words, experts believe that the Home Office’s plans to “push-back” migrant boats in the Channel will breach international law and also endanger migrants’ lives.
In September, Sonia Lenegan, legal director of the Immigration Law Practitioners’ Association, said the tactic was “extremely dangerous and will put lives at risk”.
To challenge the use of push-backs, Channel Rescue, an organisation devoted to ensuring the safety of migrants, has launched a legal case against Ms Patel.
Explaining the move, Kim Bryan, Channel Rescue volunteer, said: “We believe this proposed policy is life-threatening, inhumane and unlawful.
“We have given the Home Office until 29 November to respond to our legal challenge. If we don’t receive a satisfactory response, we will issue judicial review proceedings.”
More to follow