Mr Groves said it was not the first time a beluga has been spotted in United Kingdom waters in recent years.
Two beluga whales play together.
"Beluga whales inhabit cold, Arctic waters off Greenland, Svalbard and in the Barents Sea", the group said.
The Beluga poked its head out of the water on multiple occasions.
Tanya Ferry, environment manager at the Port of London Authority which is monitoring the whale, said it was unclear what the whale could eat.
"We would urge that the whale is given space and disturbance is kept to a minimum".
"We certainly don't want people trying to rescue it", she added.
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Can you beluga it?
Marine mammal experts at the Museum have said that it not possible to tell if the animal is definitely a beluga whale without clearer images, but they will keep an eye on its progress in the river. The last sighting of a Beluga whale was some three years ago, off the coast of Northumberland, in northern England.
The beaked whale, dubbed the Prince of Whales by some, became a sensation in London with large crowds gathering to watch the ultimately fruitless rescue attempts and near 24-hour media coverage.
The RSPCA animal welfare group said that it was "working with other agencies to monitor the situation" and sent researchers to the scene.
Belugas, also known as white whales, are "one of the most familiar and easily distinguishable" of all whales, according to National Geographic. They have a rounded forehead and no dorsal fin.
The whales were nicknamed "canaries of the sea" by early whalers due to their squeaks and squawks.