British ministers convened for emergency talks on the mounting crisis, as Prime Minister David Cameron acknowledged the situation in the northern French city of Calais was "very concerning."
The man, thought to be in his late 20s and of Sudanese origin, was apparently crushed by a truck as he tried, with hundreds of others, to smuggle himself into Britain, seen as an "Eldorado" for migrants.
Attempts to penetrate the 650-hectare Eurotunnel site have spiked in recent days, with migrants trying several times a night to outfox hopelessly outnumbered security officials and police.
Long queues formed outside a medical tent to treat those hurt overnight and doctors said they were also coming under huge pressure.
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"Our team can only treat 90 patients a day. Yesterday, we had to administer urgent treatment to 64 people," said Chloe Lorieux, from the medical charity Medecins du Monde.
Meanwhile, she deployed a team to find the dead man's family.
"It's always a sad moment but psychological support is critical," she said.
The migrant killed Wednesday was the ninth such death since June and the rising toll is creating tensions between French authorities and Eurotunnel, the firm that runs the passenger and freight service under the Channel.
"The pressure we are now under every night exceeds that which an operator can reasonably handle, and calls for an appropriate reaction from the states" of France and Britain, the firm stressed in a statement.