Should instead of would

In Red-headed League from The adventures of Sherlock Holmes, a character named Wilson describes a weird sight of hundreds of red haired men crowding the area to Holmes. By his account he had been really shocked by this crowd, yet he says 'I should not have thought there were so many in the whole country as were brought together by that single advertisement.' By context I think he means he wouldn't've thought it, but I don't...understand the use of 'should not have' here..

As the OED notes, this use of should is a colloquial expression of the "strong affirmation" of a statement. Here

I should not have thought ...

is the equivalent of

I definitely would not have thought.

In our (chiefly British) English lessons in a German high school in the late 1970s we learned that shall and its past should are simply the first person forms of "will" and "would". I think this use has since then become rare, certainly in the U.S. The use has shifted towards or focused on assertion and moral obligation ("The plaintiff shall...", "I know I shouldn't").

In your example, an American Wilson of today would probably just say "I wouldn't have thought ...".