That Keith would have never been able to play at Stephen’s house points to the strict maintenance of class difference that dictated London society. Although Keith’s parents tolerate Stephen and his daily visits, they still subtly show that they are uncomfortable with a boy of lower class, so much so that they can’t even acknowledge his presence or address him directly. But it seems that the war provides enough of a distraction or shakeup of social norms to allow Stephen to continue associating with Keith—although it’s suggested later that Stephen is being unnecessarily hard on himself, and in fact it’s
Keith who has a hard time making friends and is disliked by most of the children in the Close. This passage also introduces some information about Keith’s mother that later becomes more important.