A Kurdish woman from northern Iraq, who was among 27 migrants who died trying to cross the Channel between France and Britain this week, has become the first victim to be named by British media.

The migrants died when their dinghy deflated as they made a perilous crossing of the English Channel on Wednesday, the worst tragedy on record in one of the world's busiest shipping lanes.

Maryam Nuri Mohamed Amin, 24, made the journey in order to see her fiance, the BBC reported, citing family members and a close friend.

"When she left Kurdistan she was very happy, she couldn't believe that she was going to meet (him)," the woman's friend Imann Hassan was quoted as saying by the British broadcaster, which said her fiance already lived in Britain.

"She tried to live a better life, she chose the UK, but she died," Hassan added.

Reuters was not immediately able to verify the information.

The tragedy has further strained ties between France and Britain, with French President Emmanuel telling Britain on Friday it needed to "get serious" or remain locked out of discussions over how to curb the flow of migrants across the Channel.