The whale stayed in the same area for at least three hours, feeding around barges in the river, Andrews added, as he continued to keep an eye on the animal's whereabouts.
Belugas, also known as white whales, are "one of the most familiar and easily distinguishable" of all whales, according to National Geographic.
Whale experts said a beluga may have ended up in the Thames after becoming disorientated and making a navigational error.
A spokesman for the RSPCA said: "The RSPCA is aware of reports of a whale, possibly a beluga, in the Thames".
The extremely rare sighting triggered wonder and excitement when the whale was first seen on Tuesday, but after it was spotted again on Wednesday in exactly the same location, concerns grew that the beluga had got lost and was potentially in danger.
"Beluga whales are a species of the icy Arctic - finding one in the tepid Thames is an astonishingly rare event", said Rod Downie, polar chief adviser at WWF, the World Wide Fund for Nature.
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Belugas live in estuaries, continental shelves and slopes, and deep ocean basins in open water, loose ice, and heavy pack ice.
We would encourage people to look from the land if the whale is still close to the coast.
"We are working with other agencies to monitor the situation and ready to provide appropriate assistance if requested".
In 2006 an 18ft (5m) northern bottle-nosed whale died after becoming stranded in the Thames.
They range from 13ft (3.9m) to 20ft (6.1m) in length and have distinctive rounded foreheads.
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.