Planning permission was granted for the outward extension of the original basement by the council in 2018.
The house in Durham Place fell to the ground; no one was inside as it has been undergoing construction.
The Health and Safety Executive is investigating.
A spokesperson for Kensington and Chelsea Council says:
“Our team worked through the night, opening an emergency rest centre for those affected and assessing the safety of surrounding buildings.
“Thankfully
no-one was hurt and residents were able to return safely to their homes at 3am.
The reason for the collapse is being investigated by the Health and Safety
Executive.”