Thanks for the comment, @Geron Kees.
As far as entrenched formality and rigid uniformity is concerned, I think it's important to remember that this is set in a grammar school in England over fifty years ago. It really was a different time back then. And pupils could only enter grammar schools by passing an entrance exam (the Eleven-plus) - unless it was a private school (which, oddly enough in England is known as a Public School), in which case their parents could pay for them to attend, assuming they could afford it. One wrong step out of line by a pupil could result in them being expelled, and have to move to a secondary modern school (they were discussed in an earlier chapter's comments). Grammar schools in those days often considered themselves as being for the elite, considered themselves to be superior, and had a tendency to look down on the rest of society.
As for Lowry, I'll repeat what I said in my reply to @Daddydavek's comment, and say that all should hopefully become clear in a future chapter (perhaps even the next one).
And I'll do my best not to keep you waiting too long. The next few chapters are just about finished (just need a final polishing). But I don't want to rush them out, as that may leave readers waiting too long for me to flesh out the later chapters.