How can the reader tell that the Passage is
written from the point of view of a
nineteenth-century British child?

The user third person narrative.

Explanation:

In any literary work, when an author uses third-person he brings the thoughts of the character to the spotlight.

There's a certain probability that the author of the passage employs this method so that he is seen as been neutral in the story.

is that the whole question?

ah, shun the horrid gulf! by scylla fly.