The Trent affair was probably the closest that Britain came to intervening in the American Civil War and maybe even going to war against the Union. Although we wouldn't like to admit it now, most of the British establishment and the richer parts of British society actually felt much more sympathy for the Confederate side in the civil war than they did for the Union, and when a British mail ship was boarded by Union forces and some of its passengers arrested, it looked like war might be looming.
The passengers in question were two Confederate envoys traveling on board the RMS Trent, one of the many mail ships on which the British Empire depended to provide secure communication between its disparate parts. The envoys were journeying to Europe as part of a diplomatic offensive by the Confederacy to try to obtain diplomatic recognition from key European countries, especially Britain and France.
Had the Confederacy made more military progress in its early years then this recognition would almost definitely have been forthcoming. The upper-class Englishman who dominated Britain's political system had no sympathy for the United States, which they resented for having won its independence during the American Revolution and for the continued example of democratic government which it set for the rest of the world. For a political elite whose own population was demanding democratic freedoms, it would have been very convenient indeed for the world's foremost republic to go down in flames and hence prove the unworkability of democracy. There was also the fact that large parts of the British economy were dependent on cotton grown and exported from the American South.
This meant that until the Emancipation Proclamation made it clear that slavery stood on one side of the civil war and freedom on the other, the issues at dispute in the war were sufficiently murky that it was still possible to imagine that London might set itself decisively against the Union. Even if it didn't intervene militarily, it might arm the Confederacy or provide any other sort of help; even just recognition as an independent state by Britain, then the world's only superpower, would provide crucial moral support. As Abraham Lincoln - who, incidentally, the British elite and their flagship newspaper The Times viewed as an upstart proletarian because of his humble background - recognized, the U.S. could not afford to take on more than "one war at a time".
The decision to seize the Confederate envoys from the Trent and to hence prevent them for going to Europe to advance the South's claims was actually made independently by the captain of a Union ship rather than being ordered from Washington. But after it happened, the U.S. press erupted in a nationalistic frenzy at the fact the British had allowed the men to travel on their ship to begin with; the British press predictably erupted into a fury of its own. At first, Lincoln and his Cabinet backed the seizure of the envoys, not realizing the reaction it would bring from London.
But soon came the demand for the release of the men. Proud and at the peak of its naval might, the United Kingdom was not to be trifled with upon the seas - especially when the security of its communications and the rights of its citizens were concerned. Ironically, the seizure of men from American ships without any legal proceedings had been one of the principal causes of the War of 1812 between the U.S. and Britain; now America was doing the same thing back. Lincoln realized the untenability of the U.S. position and ordered that the envoys be released, satisfying Britain.
Lincoln saw that there was no sense in insulting the world's only superpower, that more war would not solve anything, and that the British could eventually be brought round to begrudgingly accepting the Union cause when the moral stakes of the war were made clearer; and he was proven right, as when the envoys were released and traveled to Europe they were generally ignored by the governments there. As Lincoln deftly handled the civil war over the coming years and moved to end slavery, he appeared strong and decisive, and European governments seemed to have little to gain from antagonizing him or their own populations by setting themselves against such an obviously moral cause. A little conciliation from the Union in the meanwhile had gone a long way.