67th Tigers did a horribly contrived nationalist scenario on the Trent War. A work for CJ squads of Anti-Americans, NeoConfederates, and above all, Rule Britannia Forever Britons. It is as far as I know the largest TL on AH.com covering this subject. But be warned. It is NOT for the faint of heart. It does not fit the strictest definition possible for an ASB TL, but it is a 19th century version of the Unspeakable Seamammal. Not as much in terms of what was militarily possible, but in terms of politics, economics, and logistics. Imagine a TL where the greatest general America ever produced was George B. McClellan. Imagine one where it's worst politician ever was Abraham Lincoln. You get the idea.
OTL, Palmerston and Gladstone may have privately welcomed the idea of war with the Union. But their people (outside of the more foolish elements of the aristocracy) did not. As long as Lincoln was ready to quickly compromise, nothing was going to happen. Palmerston was not an absolute monarch, and despite a flash of jingoism, the country didn't want another war just five years after the Crimean War had ended.
EDIT: "An Unfortunate Event: The Trent War" is the title. Considering how the war turned out, I have to say the author must have meant the use of the word "Unfortunate" to be supremely ironic (if not baiting in nature). His nonstop flaming of Lincoln, his cabinet, his best (and LOYAL) generals, and the whole of the Union (not to mention the USA in general in other threads) showed quite clearly that he saw absolutely nothing "unfortunate" about the destruction of the United States of America.