It is most assuredly not a good idea, in spite of the fact that I have absolutely no doubt that Britain would win-- and quickly, too. The point here being not that Britain is so strong, but that the USA is so damned weak. People tend to back-project the later, far more powerful USA onto the mid-nineteenth century, but that's a delusional venture. The USA was so weak that it took years to beat the tar out of the CSA, which mainly consisted of the least industrialised parts of the antebellum union, was run by idiots, and had to spend a lot of of its potentially available resources and man-power to keep an eye on all those slaves the whole damn time.
A war against Britain would be a
bit of a different experience than one against a bunch of neo-feudal cosplayers trying to run a country using such masterful principles as "the government isn't allowed to finance rail-roads".
Also, the US Navy was a joke, and that's a far more crucial point. Because this wouldn't be a land war. The Royal Navy showing up, sending all of the USA's ships to the bottom of the ocean, bombarding all port cities worth mentioning, and then blockading the USA would suffice. That, plus a bunch of boots on the ground in Canada to repel any ill-advised US attempts to try "
it's only a matter of marching" again. You know, since that turned out so well the last two times they tried...
Basically, this war wouldn't be a land war and certainly wouldn't be a war of conquest. It would be Britain making a point. point it would prefer not to have to make. But if forced...
"
Well, remember how, last time around, you wanted to play this silly game and then we torched your capital?"
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(And I repeat, probably superfluously, that this war would be senseless and could have no positive effects for Britain in the long term. But if forced to fight, Britain would
win.)