Brutalism apparently derived its name from the French béton brut, meaning "raw concrete", and the Trellick has this in spades. Your author has always found Brutalism particularly inspiring, and this tower is no different. It is certainly well deserving of the Grade II* listed status, which was awarded in the late 1990s.
The building has 217 flats and is characterised by a long, thin main building, with a separate tower housing a lift and linked at every third floor to main building.
The tower is at 5 Golborne Rd, W10, just up the road from Westbourne Park Tube, and you can read more about it on Wikipedia.