A passing tug saw the mammal, a young female humpback measuring around 36ft (11 metres) long, off the Isle of Sheppey in Kent.
Local navigation warnings were issued to vessels in the area to be aware of the floating carcass before it was towed to Sheerness Docks, Thames Coastguard said.
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Sussex astronaut Tim Peake's space mission will be celebrated with a free exhibition at The Novium Museum in his home city of Chichester.
Emergency rescue teams were at the scene in East Sussex.
Plenty of warm sunshine with the chance of thundery showers later.