A girl plucked from the Mediterranean this week is believed to be the sole survivor of a migrant shipwreck that was carrying 45 people.

The girl, reported to be about 11 years old, was rescued by the Trotamar III, a yacht operated by a German NGO, and brought to the island of Lampedusa, south of Sicily, early on Wednesday.

The child, who is believed to be from Sierra Leone, was kept afloat by a cheap life vest and two inflated car inner tubes that she had around her body.

She was suffering from hypothermia when she was found after the crew of the rescue yacht heard her cries for help in the darkness.

“It was an incredible coincidence that we heard the child’s voice even though the engine was running,” said Matthias Wiedenlübbert, the captain of the yacht. “Of course we looked for other survivors. But after a day-long storm with winds of over 23 knots and 2.5-metre-high waves, it was hopeless.”

The girl told rescuers that she and about 45 other migrants departed in a boat from the port of Sfax in Tunisia four or five days ago.

But when they hit strong winds and large waves, the boat – a crudely made vessel consisting of sheets of steel welded together – capsized and sank.

Katja Tempel, from Compass Collective, a rescue NGO, told The Telegraph: “She says the boat capsized three days ago and she was thrown into the water. She told us there were two other people in the water near her but after a day they disappeared. She was in the water all alone for the next two days.

“She had two car inner tubes around her waist and a very simple life vest. When we rescued her, she was totally exhausted and very cold but she could walk and she could talk.”