"We are standing by," said Tony Woodley of the British Divers Marine Life Rescue Group, which has been following the whale since it appeared on Friday in the first sighting of the endangered species in the Thames since records began nearly a century ago.

"We have a flood tide now and no beaches so the whale will be in deeper water," Woodley said.

"We cannot just leap in and grab the animal while it is free-swimming," he added, explaining that it would be too stressing for the whale and possibly dangerous for the rescuers.

The 15- to 20-foot (4.5- to six-metre) long mammal, which normally lives in deep water, grounded on mudbanks several times on Friday but managed to free itself each time.

But it is thought to be injured and tired, and the falling tide could cause it renewed problems.

Early Saturday the animal was spotted in the vicinity of Vauxhall Bridge upstream of the most famous landmarks like the Houses of Parliament and the London Eye ferris wheel.