It broke out just after midnight at a five-storey converted terraced house.
15 engines and around 100 firefighters attended.
Crews say it’s too early to say how it started.
Kensington and Chelsea Council staff were deployed to the site of the fire, and then later in larger numbers to the Double Tree Hotel nearby, where residents initially sheltered.
The authority says a support team has now established a more permanent base and is offering support at the Millennium Hotel, with a large number of rooms booked and ready.
Alongside staff, deputy leader Cllr Kim Taylor-Smith and ward Cllr Sam Mackover have been working to support residents and speak to people about what they need.
There are between 75 and 150 people to potentially help and support.
