The four metre-long mammal, which was rescued overnight after it was first spotted on Sunday lunchtime near Barnes Bridge, is said to have escaped an inflatable cushion that was guiding it while it was being towed to safety at 1am.
Now rescuers are attempting to save the whale, which usually lives in the open sea, for the second time.
Glen Nicolaides from London Fire Brigade told the broadcaster that before its escape, the whale was in the process of being moved to a more stable area where the scale of its injuries, and whether it could be released, would be investigated.
The new rescue comes after hundreds of people gathered on the riverbank on Sunday when the minke whale became stuck on the boat rollers at Richmond Lock and Weir.
Conservation experts believe it is the furthest upstream that any whale has even been seen in the Thames.
Jake Manketo, 20, from Richmond, said: “We couldn’t believe our eyes when we first saw the poor fella — it’s not every day something like this happens in Richmond.”
It was hosed down to keep it cool while a vet carried out checks at the river’s edge. The whale had been thrashing around in between periods of apparent lifelessness.
Minke whales are the smallest of the great whales, growing to about 10 metres and are usually found in the northern Atlantic and Pacific Oceans.
The whale was towed to deeper waters near Isleworth where it slipped loose at about 1am.
A spokesman for the Port of London Authority said the whale’s life still “hangs in the balance” as it is so far from its natural habitat. He told MyLondon: “To a certain extent all we can do now is let nature take its course. The whale is in quite a predicament, so we’ll have to see.
“Its injuries aren’t massive or obvious but it is compromised in the sense of minor cuts and things. In a more general sense it’s in a stressed and weakened situation and isn’t where it should be.” Whales regularly get lost in the Thames, although it is rare for them to be seen so far from the estuary.
In 2018, a beluga whale, nicknamed Benny, survived in the Thames for three months and was regularly spotted swimming and feeding in the Kent stretch during November and December. In 2006, thousands of people gathered to see a northern bottlenose whale which swam up the Thames to central London.
Despite rescue attempts it died, with its skeleton going on show at the Natural History Museum.