There are no reported injuries.
The crane was working on a James Taylor Homes development in Kingston upon Thames.
Residents of neighbouring Fassett Road were temporarily evacuated while the fire brigade attended the scene.
A London Fire Brigade spokesperson said: "We were called at 16.15 to reports of a tower crane collapsing into a building under construction on Beaufort Road."
A Metropolitan Police spokesperson said: "Police were called shortly after 4pm on Tuesday December 10 to reports of a partially collapsed crane on a building site on Fassett Road in Kingston. Emergency services on the scene. At this early stage, there are no reported injuries. A number of local residents have been evacuated as a precaution."
James Taylor’s development, called The Harriers, comprises 60 flats and 16 new houses and the refurbishment of three existing houses, due for completion before the end of 2020.
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