In The Long Dark Tea Time of the Soul, Gently finds a teenager watching TV upstairs who headbutts him when he turns off the TV.
How does the teenager relate to anything else in the plot? Was he Anstey's son or something?
The author makes it clear that the boy was Anstey's son. There is a marked family resemblance and he lives in the house. Given his living conditions and mental state, it's fairly evident that he's a typical antisocial teenager (living in his bedroom, ignored by his high-flying father).
His subsequent violence may be a result of mental deficiency or the trauma of having discovered his father murdered:
After he's taken away, there's no further mention of him. He doesn't relate to the plot at all, other than giving us a greater insight into Anstey as a driven, callous individual.