The latest tragedy in the Channel underlines the need to work together more closely, ministers say.
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The UK and France has pledged to “destroy” the business model of people-smuggling gangs after at least four people died when a migrant boat got into difficulty in the Channel.
The rescue operation will resume later for up to four more people lost at sea.
Thirty nine people were rescued from freezing waters on Wednesday.
Home Secretary Suella Braverman and her French counterpart Gérald Darmanin said this highlighted the need to jointly prevent the crossings.
A charity which offers support to migrants in Calais, Utopia 56, said on Wednesday it had received a voice message from a man believed to be on the sinking boat.
As babies could be heard screaming in the background, he pleaded: “We have a problem. Please help. We have children and families in a boat. We are in the water.”
The charity said it had tried to respond but had been unable to make contact.