As someone living in an ex-local authority low rise flat I've been surprised that I haven't heard much mentioned about the following.

When CFCs were banned the gas used in fridges was replaced by a much more flammable gas that fire authorities have noted as potentially more dangerous because of the intensity of any fire.

Although in my block each flat is isolated with concrete floors / ceilings and brick dividing walls the flats are connected vertically by the service ducts which in this and other blocks I've seen are situated in the kitchen.  To provide some storage space the duct is partitioned by ply-wood from a cupboard with gas and electric meters.  As storage space is limited the cupboard is crammed with all kinds of flammable material.

The other point that seems to have been largely ignored is the weather..  This disaster happened at night, during a heat-wave.  In my block every flat had doors and windows open to get a draft of cool air circulating.  In the tower block it would have been the same and once a fire started the flames would have been fed by the up-draft.  Once a fire gets into a service duct it would be sucked upwards with flammable partitions on every floor and no fire resistant barrier into the cupboards. 

Although the fire was visibly racing up the external cladding this must have also been aided by the air sucked in through open windows feeding the fire inside.  I can't help thinking that the fire would not have spread so fast if it had happened in winter when most of the windows would have been closed.