High rise fire

This tragic London apartment tower fire raises the question - what is it that burns so well in a tower block like that?   I reckon that the sight of a high rise almost entirely on fire internally is shocking because I would normally assume that it would mainly be only furnishing and curtains that can really burn well, so shouldn't any fire be readily contained to within one apartment, or at worst, one floor?  

But it obviously doesn't work like that...

I see that there is a Wikipedia entry up for the Grenfell Tower fire already, and it notes this:

In November 2016, a residents organisation, Grenfell Action Group, published online an article attacking KCTMO as an "evil, unprincipled, mini-mafia" and accusing the Borough Council of ignoring health and safety laws. The Group suggested that "only a catastrophic event will expose the ineptitude and incompetence of [KCTMO]". The group had also published articles criticising fire safety and maintenance practices at Grenfell Tower.^[12][13]

This is going to be in the news for quite a long time, by the sounds.