For anyone twitching the Beluga it's been feeding around the barges for the last hour and hasn't moved more than 200m in either direction.
By Tuesday lunchtime, photographers were lining the banks of the Thames, as were locals and others, and the BBC had launched its own live-stream of the creature, with some folks giving themselves the afternoon off work just to watch it.
Rescue teams are on standby in case the whale gets into danger.
Whale experts said a beluga may have ended up in the Thames after becoming disorientated and making a navigational error.
"Beluga whales are an Arctic species, often seen in groups".
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The sight of a beluga whale so far south - 1,000 miles (1,600 kilometres) from even Iceland - is exceptional.
"This is the most southerly sighting of a beluga we have ever seen around these shores", Lucy Babey, head of science and conservation at the ORCA charity, was quoted as saying by The Mirror newspaper.
The RSPCA animal welfare group said that it was "working with other agencies to monitor the situation" and sent researchers to the scene. "There have only been around 20 sightings of beluga whales off the United Kingdom coast previously, but these have occurred off Northumberland, Northern Ireland and Scotland".
"He or she is obviously very lost and quite possibly in trouble".
After British Divers Marine Life Rescue were alerted, they confirmed the sighting, noting that the whale seemed to be "swimming strongly".
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"We would urge that the whale is given space and disturbance is kept to a minimum".
A bottle-nosed whale became stranded in the Thames for two days in 2006, but died from convulsions as it was being rescued.
They range from 13ft (3.9m) to 20ft (6.1m) in length and have distinctive rounded foreheads.
They are common to Alaska, Russia, Canada, and Greenland.
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