Crews were called to Long Drive, Northolt, northwest London at around 11.30pm on Monday and multiple units are alight.
London Fire Brigade said 15 engines were sent to the area.
Station manager Ben King said: “This is a very visible fire.
“We would advise nearby residents to keep their windows closed as there is a lot of thick smoke in the area.
“We have a lot of fire engines on the scene so people should avoid the area where possible.”
The cause of the fire is currently not known.
Firefighters are expected to be at the scene for most of the night, and around a third of the building is alight.
Mr King said: “Crews are working hard to prevent the fire spreading to other units. We are likely to be on scene for a number of hours.”
At 3.30am, London Fire Brigade said additional crews were sent to the fire, bringing the total number of firefighters to 120.
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