If confirmed, the woman's death would be the first casualty in what is one of the world's busiest shipping lanes.
Lisa Doyle, director of advocacy at Britain's Refugee Council, called for “more safe and regular routes of travel” for migrants, warning that the trip through heavy marine traffic was “treacherous”.
“This border kills, silently,” said Calais Migrant Solidarity, a French non-governmental organisation, protesting against border enforcement policies it says are becoming “more and more violent”.
British rescuers launched a search last Friday after reports that three people with life jackets had fallen into the sea from a boat carrying migrants across the Channel.
Two of the missing migrants were found but a woman remained unaccounted for. The search, which also involved Belgian and French coastguards, was suspended on Saturday.
The UK Home Office interior ministry on Monday said a “thorough and extensive” air and sea search had been carried out and it would pursue an investigation into the incident.
“Crossing the Channel in a small boat is a huge risk. The criminal gangs who perpetuate this are ruthless and do not care about loss of life,” the ministry said in a statement.
Dozens of migrants have made the crossing in recent days.
Two were intercepted by British border guards last week crossing the 33km waterway in a kayak.
French authorities also last week rescued 11 migrants attempting the crossing after their boat capsized.