The International Organization for Migration said it was the biggest single loss of life in the Channel since it began collecting data in 2014.
Prime Minister Boris Johnson said he was “appalled” by what happened, adding the UK would leave “no stone unturned” to stop human trafficking gangs.
The dead include five women and a girl, the French interior minister said.
Gerald Darmanin also said two people were rescued and one was missing.
Four people had been arrested near to the Belgian border, he added, saying: “We suspect that they were directly linked to this particular crossing.
A fishing boat sounded the alarm on Wednesday afternoon after spotting several people at sea off the coast of France.
French and British authorities are conducting a rescue operation by air and sea to see if they can find anyone.
Mr Johnson said the deaths were a “disaster”, adding that it was vital to “break” the people trafficking gangs which, he said, were “literally getting away with murder”.
Speaking after chairing an emergency Cobra meeting, the prime minister said more needed to be done to stop criminals organising crossings.
“It also shows how vital it is that we now step up our efforts to break the business model of the gangsters who are sending people to sea in this way,” he said.
French prime minister Jean Castex said the shipwreck was a “tragedy” and those who died were victims of “criminal smugglers”.
“My thoughts are with the many missing and injured, victims of criminal smugglers who exploit their distress and injury,” he said.
French President Emmanuel Macron said: “France will not let the Channel become a cemetery.”
He promised to “find and condemn those responsible” for the tragedy.
Mr Macron also called for an “emergency meeting of European ministers concerned by the migration challenge”.
Jean-Marc Puissesseau, president and chairman of the ports of Calais and Boulogne, told BBC News 50 people had been on the boat, and about “five or six” people had been found.