The Civil War in America absolutely dominated the British national conversation, especially in the early years of the war. Politicians followed the conflict closely, and there were even several debates in Parliament over British policy toward the conflict.
Frequently discussed was a line that a lot of Americans would recognize today, of "when should Britain get involved??" because of the destructiveness of the conflict. Prime Minister Palmerston & Foreign Secretary Russell spent a lot of time maneuvering and deflecting calls for Britain to get involved or pick a side.
A few other bits I found surprising when studying this topic—
1. Some British MPs were very pro-Confederate, and pushed for recognition of the Confederacy as a real country in Parliament.
2. British war correspondents were on the ground with both Union and Confederate armies, and sent regular dispatches to British newspapers.
3. British (and other European) officers regularly volunteered on *both* sides.
4. It was fashionable for a time in Britain to be pro-Confederate. Confederate propagandist networks *in* Britain brilliantly played down slavery and played up "self-determination".
5. Britain nearly declared war on the Union (Trent affair), to the point that Royal Navy was just waiting for the go-signal to commence hostilities & Britain sent thousands of additional troops to Canada.
6. There were *tons* of ironclads already in European fleets, there had just never been a fight between ironclads! Europeans watched the Monitor v. Merrimack battle & adapted their fleets & battle doctrines accordingly.
7. The British cabinet had a very serious, "can we even win a war against the U.S. anymore?" conversation at the end of the conflict, after witnessing the million-man army of the Union, the Richmond campaign, and growing effectiveness of the U.S. Navy.
8. Americans credit Seward as a brilliant Secretary of State during the conflict, but in Britain and France he was considered foolish, dangerous, and unpredictable—a lot of the tension between the Union and Europe can be laid at his feet.
9. Prussian military observers watched how the Union used railroads to move massive numbers of troops & supplies around, and adopted a lot of the Union tactics to absolutely crush the French just a few years later. (Franco-Prussian war of 1870.) Seriously - there were European observers *all over the place*.