The RSPCA said: "We are working with other agencies to monitor the situation and ready to provide appropriate assistance if requested", it said.
Rescue teams are on standby in case the whale gets into danger.
According to National Geographic magazine, beluga whales can range from 13 to 20 feet in length.
Babey said it was unclear why this one had lost its way and come into the Thames, though it would be unlikely to have lost its way due to storms or because it was following prey.
Marine mammal scientists at the Whale and Dolphin Conservation has been monitoring the wale in case it "live strands" on the sandbank.
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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 would urge that the whale is given space and disturbance is kept to a minimum", he said.
In 2006, a whale died after it swam up the river into central London despite rescue efforts. They have a rounded forehead and no dorsal fin. They are known for living long lives and are typically found further north, in Arctic waters.
Belugas, which can grow up to 5.5 metres (18 feet) long, spend most of their time off the coasts of Alaska, Canada and Russian Federation, though they often travel great distances in search of food.
Belugas are able to produce sounds such as chirps, clicks, whistles and squeals, giving them the nickname "the canary of the sea".