My research is on the history of bread in Britain from 1846 to 1914, but unfortunately I cannot offer much in the way of an answer. I can tell you that in my research, outside of some middle and upper-class cookery books, I've come across exactly zero references to sandwiches. Now, absence of evidence is not evidence of absence, but as far as I can tell, for most Britons in the second half of the nineteenth century, sandwiches were just not a thing.

We could speculate all day about why the sandwich was pretty much reserved for those of means, but my money would be on the invention of sliced bread. This happened in tbe US in the 1920s, and was part of a whole movement to create "modern," machine-made bread. It was popular but probably not ubiquitous until after the war. My guess is that prepackaged, sliced bread, baked in tins and with relatively soft crusts, combined with rising living standards on both sides of the Atlantic to produce sandwiches.

Check out Aaron Bobrow-Strain's book White Bread: A Social History of the Store-Bought Loaf.