Assuming the war happens at its most plausible from some really, really shitty miscommunications and much idiot-ball grabbing on all sides, the war will play out thus: war with Britain overstretches the Union's war economy at its most fragile, an impending CS victory and foreign recognition nips quite a bit of the more destabilizing and destructive anti-CS sentiment among Southern whites in the bud, and the USA politically has already lost the war no matter what it does on land or sea. If the Union Army of 1861 goes to war with the UK, its mostly inexperienced leadership and rank and file will be massacred by British regular professional troops, and the US Navy will be sunk in short order by the Royal Navy in the last great war of wooden ships and iron men.
The ultimate winners are the Hohenzollerns and the Romanovs/whatever, if anything, succeeds them as rulers of Russia, the ultimate loser is democracy as an ideology.