There are a number of indications in the story that Mr. Nilson enjoys a high social status. For one thing, he's "well-known in the City." This is a reference to the City of London, the famous financial district in Britain's capital city, the British equivalent of Wall Street. If Mr. Nilson is indeed a well-known figure in this part of the world, then we can reasonably infer that he's a wealthy, important man, perhaps a banker or a financier. Our initial impressions are further confirmed by his using an ivory-backed hand mirror. This is clearly the kind of luxury item that one would normally associate with the wealthy upper-classes. A further example of Mr. Nilson's exalted social status comes in the following sentence:
In the dining-room his morning paper was laid out on the sideboard.
The implication here is that Mr. Nilson's morning paper has been laid out for him by a butler or some other servant. Again, this would suggest his membership of the social elite.