In addition to the general topical interest indicated in the title, I am also curious about British mathematics of the period viewed through the lens of competition with the rest of Europe (and perhaps even the rest of the world). For example, I have often heard it argued (informally) that the whole Newton-Leibniz-calculus kerfuffle can only be properly viewed in terms of a more general conflict between British and European mathematicians and scientists in that time period. Are there any books which address the existence and historical importance of such a conflict?
The books on history of mathematics are not normally divided by national boundaries. I do not know of any book addressing specially the history of British mathematics, or German mathematics, or French mathematics. (Exception is Russian mathematics:-) Mathematics is not really divided on national lines, this is an international enterprise, at least in Europe, at least since 18th century. So 19 and 20 century European mathematics is a single thing, with no national divisions. Mathematical journals, from the very beginning were international, and published papers from all countries.
A good book on 19 century mathematics is Klein, History of mathematics in 19th century (there is an English translation). It addresses German, British, French and Italian mathematics, and of course Norwegian too.
Here are two references, from a broader perspective:
"Mathematical Visions: The Pursuit of Geometry in Victorian England" by Richards.
"Mathematics in Victorian Britain", ed. by Raymond Flood, Adrian Rice, Robin Wilson.