Over 30 people battled to save the six-ton whale for about 12 hours, until tests revealed the creature was suffering from irreversible renal failure, caused by dehydration and hunger. Its condition was also aggravated by the compression of its organs under its own body weight.
Although the whale was successfully refloated, it was too late to save its life.
"The tides are dropping at the moment and at some point we will be able to administer the legal injection," Paul Jepson, a vet from the zoological society of London, said.
"The lethal injection is just a powerful anesthetic, so it won't be painful to the whale in any way," he added.
Vets believe that the whale may have already been ill before becoming stranded. It had not eaten or drunken for several days, as it gets fluids from deep-sea squids which are not found in the English Channel.
In January 2006, a whale of the same species died despite a massive and highly-publicized rescue attempt in the River Thames.