After a two-day battle to save the injured animal, experts say the whale would likely starve if it was released back into the sea.
The British Divers Marine Life Rescue says 'Hessy' had come up the river because they were lost or ill.
The highly unusual sight has been confirmed by British Divers Marine Life Rescue.
The death is not being treated as suspicious.
Soaring temperatures in London meant thousands of people headed to the river to cool down.
London's super sewer stretches for 15 miles alongside the capital's river.
Majority Of Litter In The Thames Found To Be Single-Use Plastic – Time To Ditch Those Bottled Drinks, Wet Wipes And Crisp Packets
More than three quarters of rubbish was plastic.
A 5,600-year-old skull fragment, found by a mudlarker on the south bank of the Thames, will go on display at the London Museum. Carbon dating shows that the skull belonged to a man who was over the age of 18. It is one of the oldest bone fragments ever found in the Thames.
The Neolithic discovery was made by a mudlark.
Lindsey Cole initially thought the animal was a sheet of white plastic.