The Maritime and Coastguard Agency (MCA) said drones were used in an overnight search and ships have been asked to post lookouts to help with the effort.

The MCA also said helicopters and ships had been deployed to the area where the small boat ran into difficulties in the early hours of Wednesday morning.

The boat was carrying up to 50 people - including, it is believed, women and children - when it ran into difficulties.

An MCA spokesperson said on Thursday: "The search has continued overnight utilising a combination of aerial search assets and broadcast action requesting shipping in the area to post lookouts and report any sightings to Dover Coastguard.

"Our thoughts are with those affected by this tragic incident and with the families of those who have lost their lives."

The Royal Navy, French navy, Coastguard and RNLI lifeboats were all involved in a major rescue operation off the Kent coast on Wednesday after authorities were alerted at 3.05am to a "small boat in distress".

Coastguard rescue teams from Deal, Dungeness and Folkestone have been involved in the operation, along with helicopters from Lydd and Lee-on-the-Solent, and another from the French navy.

Initially it appeared that 43 people had been rescued, but the figure has since been revised to 39 after information from various agencies was updated.

Two casualties were taken to the William Harvey Hospital in Ashford, bosses there said. One was later discharged but the other had died by the time they arrived, it is understood.

A British fisherman whose crew saved 31 people told Sky News he was woken in the early hours of the morning when migrants surrounded his boat "screaming for help" - and a French charity say they received a mayday call.

The boat's skipper Raymond said he then counted 45 people holding onto the collapsed dinghy and surrounding his fishing boat.

Exclusive footage obtained by Sky News shows the moment of the rescue - with scores of people crammed into the small rubber boat shouting for help, as they are pulled to safety on board a nearby fishing vessel.

Read more: What has changed since 31 people died crossing the English Channel in a small boat?

Raymond said those he rescued came from Afghanistan, Iraq, Senegal and India, and told him they had each paid £5,000 to a smuggler in France for passage into the UK.

And a French charity which helps migrants in Calais said it received a 22-second WhatsApp voice note at 2.53am from a man on a sinking migrant boat begging for help as babies screamed in the background.

The man said people were in the seawater which had entered the vessel and begged the charity to "help us, help us", according to Nikolai Posner, a spokesman for the Utopia 56 charity.

The charity said the man had also sent the location of the boat. Utopia 56 tried to respond and did not receive an answer and called the French coastguard at 2.57am French time and then emailed the French and British coastguard at 3.13am.

Mr Posner said it first informed the French coastguard because "the first location that we had was in French waters".

Prime Minister Rishi Sunak expressed his "sorrow" at the "capsizing of a small boat" in the Channel on Wednesday, telling MPs there had been a "tragic loss of human life".

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There are likely to have been freezing temperatures in the Channel overnight as a cold snap was sweeping across the UK.

The tragedy came a day after Mr Sunak unveiled a raft of new measures which he said would were aimed at curbing Channel crossings.

More than 44,000 people have made the dangerous crossing this year, government figures show.

More than 30 migrants died when a dinghy sank while heading to the UK from France in November last year.