RNLI and Border Force officials found the migrant’s body floating close to the machine.
It is thought the unidentified man, believed to be in his early 20s, was thrown from the jet-ski as it was hit by a wave.
A source said: “We presume the jet-ski was stolen so he didn’t know there wasn’t enough fuel to reach Dover.
Chaos “Border staff from all over the UK have been dispatched to Dover to cope with the sheer volume of people currently trying to make crossings. It’s total chaos.”
Some 1,185 people reached the UK aboard small boats on Thursday, a new record for a single day in the current crisis.
This year more than 23,500 people have now reached the UK after crossing the Channel in this perilous way, data suggests.
A flurry of crossings over the last two weeks have reignited tensions between Britain and France over the issue.
French interior minister Gerald Darmanin blamed Britain’s work market for enticing people.
The Prime Minister’s official spokesman said the Home Secretary was seeking emergency talks with her French counterpart.
He said: “We are providing funding to the French to allow them to increase surveillance and their police presence.
“Clearly more needs to be done.”