'For anyone twitching the beluga, it's been feeding around the barges for the last hour and hasn't moved more than 200 metres in either direction.
Whales are rarely seen in the Thames, and the sighting has sparked conerns for the beluga's health.
Scientists said beluga whales are usually very social so seeing one by itself is also "concerning".
However rescue teams were on standby in case the animal got into danger.
Belugas live in estuaries, continental shelves and slopes, and deep ocean basins in open water, loose ice, and heavy pack ice.
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.
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Tanya Ferry, environment manager at the Port of London Authority, said it was unclear what the whale could eat.
He urged people to give the whale "space and minimise disturbance".
Beluga whales were last spotted in the United Kingdom three years ago off the coast of Northumberland and Northern Ireland, but sightings were "extremely rare", spokeswoman Julia Cable said.
"We are working with other agencies to monitor the situation and ready to provide appropriate assistance if requested".
Known as the "canary of the sea" due to their chirps, clicks and whistles, beluga whales can range from 13 ft to 20 ft in length and have distinctive round foreheads, known as "melons".
They are common to Alaska, Russia, Canada, and Greenland.