What does "to the prejudice of discipline" mean?

In this case:

  • prejudice means "detriment; damage".

prejudice:

  • [..]
  • damage or injury; detriment: a law that operated to the prejudice of the majority.
  • to the prejudice of: to the detriment of.

(source)

  • discipline means "behavior in accord with rules of conduct".

  • "to the prejudice of discipline" means that the discipline suffers because the newspaper office attracts all kinds of people. The next sentence from the book shows an example of this:

Zenana-mission ladies arrive, and beg that the Editor will instantly abandon all his duties [..]