The association had volunteers trained to deal with whale strandings and a rescue boat at the ready.
Although he said the appearance of blood in the water might not be as serious as it looked, he also warned that the whale might not survive the ordeal.
The animal's delicate skin which is prone to abrasions, combined with "very red blood", made even a very small injury produce a large amount of blood, "and it could look possibly worse than it actually is" Mr Woodley said.
Two options available were refloating the whale back to deep water, which he described as very tricky, or putting it down.
"The other option is if the vet is of the opinion that the animal isn't going to survive...that we would actually put it down.''
The size of the animal would make any rescue difficult.
The curator of London Aquarium, Paul Hale, said: "This is a very active swimming animal and it's not going to go anywhere it doesn't want to go so we have to persuade it to swim back out.
"I think it's going to be a tricky time for the guys that are dealing with it."
The Zoological Society of London sent its marine mammal veterinary pathologist, Paul Jepson, to the banks of the Thames to assist with the rescue.