The deaths occurred when a boat carrying 112 people set out to cross one of the busiest shipping lanes in the world and panic took hold among the passengers not far from the shore.
Rescuers picked up 49 people, with four taken to hospital, but others stayed on the boat, determined to get to Britain.
The French coastguard continued searching for any survivors.
"The engine stopped a few hundred meters away from the shore and several people fell into the water," local prefect Jacques Billant told reporters.
The coastguard said 58 people had stayed aboard the boat that left from Wimereux, about 32 km southwest of the French port of Calais.
"They did not want to be rescued, they managed to restart the engine and headed toward Britain," Billant said.
The Rwanda deportation bill — a flagship policy of Britain’s Conservative government that aims to curb irregular cross-Channel migration from northern France — cleared its final hurdle after a marathon late-night parliamentary tussle on Monday.
Under the plan, many undocumented asylum seekers arriving in Britain would be sent to Rwanda, where their claims would be examined and, if approved, allowed to stay in Rwanda.
Prime Minister Rishi Sunak says deportations are expected to begin within 10-12 weeks, with migrants identified for the first flight due to be detained and held starting as early as this week.
Rwanda said it was "pleased" to see the bill passed and was looking forward to "welcoming those relocated to Rwanda."
But senior United Nations officials warn that the plan threatened the rule of law and set "a perilous precedent globally."
In a joint statement, Filippo Grandi, the U.N. High Commissioner for Refugees, and Volker Turk, the U.N. High Commissioner for Human Rights, called on the Britain to instead take other measures to address irregular flows of migrants and refugees.
The move would have a harmful impact on human rights and refugee protection, the U.N. officials said.
The Council of Europe also called for the new law to be scrapped and said it raised "major issues about the human rights of asylum seekers and the rule of law more generally."
Sunak said the "landmark legislation" would deter record numbers of migrants crossing the Channel from northern France, and disrupt people-smuggling gangs behind them.
It also gives decision-makers on asylum applications the power to disregard sections of international and domestic human rights law to get around a U.K. Supreme Court ruling that said sending migrants on a one-way ticket to Kigali was illegal.
But the government faced a parliamentary battle to do so, with the upper chamber House of Lords, which scrutinizes bills, repeatedly sending the proposed legislation back to the lower House of Commons with amendments.
Peers, who had criticized the bill as inadequate, notably wanted a requirement that Rwanda could not be treated as safe until an independent monitoring body said so.
Members of the elected Commons, where the Tories have a majority, voted down every amendment and asked the Lords to think again in a back-and-forth process known as "parliamentary ping pong."
Sunak's government, facing what opinion polls say will be a defeat in a general election later this year, has been under mounting pressure to cut record "small boat" arrivals, particularly after a promise of a tougher approach to immigration after the United Kingdom left the European Union.
The Rwanda plan was first proposed in 2022, but has been beset by legal challenges ever since and two years on, no migrants have been deported.
The National Audit Office, a public spending watchdog, has estimated it will cost the U.K. £540 million ($665 million) to deport the first 300 migrants— nearly £2 million per person.
Migrant aid groups have said the plan is unworkable and, given the small numbers involved, would do little to cut the backlog of asylum claims.
Rwanda— a tiny nation of 13 million people — lays claim to being one of the most stable countries in Africa. But rights groups accuse veteran President Paul Kagame of ruling in a climate of fear, stifling dissent and free speech. His government has denied such allegations.
Sunak's plans could still be held up by legal challenges, while U.N. rights experts have suggested that airlines and aviation regulators could fall foul of international human rights laws if they take part in deportations.
Information for this article was sourced from Reuters and Agence France-Presse.
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