U.S. Civil War: The US-Russian Alliance that Saved the Union
http://www.voltairenet.org/U-S-Civil-War-The-US-Russian
That was a very different Russia back then. But I think America would still have evolved in a similar fashion. A governing Monarchy far away and out of touch, looking to fill royal coffers would probably resulted in the same frustration and anger.
There is no way Britain would have declared war on the Union. The political elite may have been pro-south, but the working classes, even those in Lancashire suffering most from the cotton famine viewed Lincoln as a hero (there is a statue of him in Manchester to this day) there would have been riots and maybe a civil insurrection in Britain itself if HM government had intervened on behalf of the slave owning South.