London Fire Brigade has debriefed journalists at the Cambridge Road estate.
Spokesman John Lalor said the first of many calls came in at 4.47pm of a fire at Madingley.
He said firefighters were confronted with a fire on the 12th floor.
They employed high rise procedures and said there were 100 firemen on the scene and 20 fire engines tackling the blaze from the 12th floor to the 15th and on to the roof.
Mr Lalor said no people were thought to be involved in the fire and that firemen had searched the flats and they are clear.
The last licks of flames were being put out on the roof at about 7.45pm.
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