A number of people were headed for the UK when their boat capsized in the strait.
A fishing boat sounded the alarm earlier on Wednesday after spotting several people at sea off the coast of France.
A rescue operation was launched near the port of Calais with three helicopters and three boats deployed to take part in the search.
French Interior Minister Gerald Darmanin said 31 people drowned after the boat capsized in the Channel, including five women and a little girl.
At a press conference following the event, Prime Minister Boris Johnson labelled the sinking as “disaster”, adding that it was vital to “break” the people trafficking gangs which, he said, were “literally getting away with murder”.
He said the deaths “underscored how dangerous it is” to cross from France.
Speaking to reporters at Downing Street, Johnson admitted efforts to stem the flow of migrants crossing the Channel in small boats “haven’t been enough”. He said: “I just want to say that I’m shocked and appalled and deeply saddened by the loss of life at sea in the Channel.
“I think the details are still coming in but more than 20 people have lost their lives.
“My thoughts and sympathies are first of all with the victims and their families. It’s an appalling thing that they have suffered.
“But I also want to say that this disaster underscores how dangerous it is to cross the Channel in this way.
“What this shows is that the gangs who are sending people to sea in these dangerous crafts will literally stop at nothing.
“But what I’m afraid it also shows is that the operation that is being conducted by our friends on the beaches, supported as you know with £54 million from the UK to help patrol the beaches, the technical support we’ve been giving, they haven’t been enough.”
France’s prime minister said the shipwreck on Wednesday was a “tragedy” and his thoughts were with “victims of criminal smugglers who exploit their distress and injury”.
President and chairman of the ports of Calais and Boulogne, Jean-Marc Puissesseau said: “What I know is that there were 50 people on this boat.
“What I have heard is that there are 30 people who have died, and about five or six who have been found.”
He added: “I think the people who are paid by the migrants to get to your country, with such bad weather, with such rough sea, they are murderers.
“They are really murderers.
“They don’t have any success trying to cross with these weather conditions. The sea is cold and the waves are big.
“They are murderers, and the poor migrants who have spent months and months to come to here, and who die so close to their dream… I don’t know what to do really.”
Franck Dhersin, the vice-president of mobility, transport infrastructure and ports in the Hauts de France region and mayor of Téteghem confirmed that around 50 people were believed to be on the boat.
Downing Street confirmed that Prime Minister Boris Johnson would chair a meeting of the Cobra emergency committee in response to the migrant deaths in the English Channel.
Dover MP Natalie Elphicke said: “This is an absolute tragedy. It underlines why saving lives at sea starts by stopping the boats entering the water in the first place.
“As winter is approaching the seas will get rougher, the water colder, the risk of even more lives tragically being lost greater.
“That’s why stopping these dangerous crossings is the humanitarian and right thing to do.”
Shadow home secretary Nick Thomas-Symonds said action was needed to disrupt the flow of migrants before they reached the Channel coast.
“It really now has to act as the most tragic of wake-up calls to redouble our efforts to make sure that people are not out on the water in these terrible makeshift boats risking their lives,” he told the BBC.
“It is unrealistic to think that the entirety of that coastline can be patrolled. We need to be looking at practical law enforcement action away from the coast as well.
“We need that wider joint law enforcement work with the French authorities to be disrupting further away from the coast. In addition to that we do need to look at safe and legal routes.”
Enver Solomon, chief executive of the Refugee Council, said: “It’s heartbreaking to hear that the lives of more ordinary people have been lost on a harrowing journey to Britain in search of safety.
“How many tragedies like this must we see before the Government fundamentally changes its approach by committing to an ambitious expansion of safe routes for those men, women and children in desperate need of protection?
“Every day, people are forced to flee their home through no fault of their own. Now is the time to end the cruel and ineffective tactic of seeking to punish or push away those who try and find safety in our country.”
British Red Cross chief executive Mike Adamson said: “Reports of more lives lost today in the English Channel are truly heartbreaking and come far too soon after other recent deaths on this route.
“Our thoughts are with their loved ones, who may not even know yet what has happened.
“Nobody puts their life at risk unless they are absolutely desperate and feel they have no other options.
“Everyone deserves to live in safety and it should be unacceptable to us that people have no choice but to make dangerous crossings in their search for this.
“There are no simple answers, but we urge the Government to rethink its plans for making the UK’s asylum system harder to access.
“This should start with ambitious plans for new safe routes and a commitment to resettle 10,000 people a year.”
Tom Davies, Amnesty International UK’s refugee and migrant rights campaign manager, said: “We are deeply saddened by the loss of these lives. Our thoughts are with the family and friends who have lost their loved ones.
“How many more times must we see people lose their life trying to reach safety in the UK because of the woeful lack of safe means to do so?
“We desperately need a new approach to asylum – including genuine Anglo-French efforts to devise safe asylum routes to avoid such tragedies happening again.”
A number of people are also believed to have reached Britain in small boats on Wednesday, with people seen being brought ashore in Dover by immigration officials.
The Dover Strait is the busiest shipping lane in the world and has claimed many lives of people trying to cross to Britain in inflatable dinghies.
More than 25,700 people have made the dangerous journey to the UK in small boats this year – three times the total for the whole of 2020.
This week, Home Secretary Priti Patel described the number of illegal migrants departing France as "unacceptable".