OTL in the Second Boer War the British deployed 347,000 regulars of which 7,000 were Canadian. When mobilised Empire could thus deploy 400,000 troops (110,000 Canucks, 290,000 whites from the rest of the Empire), ie twice the USA reserve.
How likely are the British to be willing to fully mobilize though? There's no vital British interest at stake in this conflict if the U.S. doesn't attack Canada and helping a slave power expand its territory is going to be deeply unpopular in Britain even before the war sends the cost of grain skyrocketing in Britain. (Which it inevitably will. OTL the British were seriously dependent on U.S. grain exports in the 1880s as 62.8% of their population was dependent on grain imports, and the British imported almost twice as much grain from the U.S. as they did from Russia, Germany, Canada, India, Australia, and Argentina combined). Nor is there any reason to believe the British are any less dependent on U.S. grain exports in TL-191 circa 1881. (Given how accommodating the U.S. was to the Confederates pre-Blaine, the British had no reason to develop alternative sources of supply prior to the Second Mexican War.)
http://www.economics.ku.dk/research/publications/wp/2004/0428.pdf pg. 8
https://books.google.com/books?id=4...VSwCm8Q6AEILDAA#v=onepage&q=1,753,000&f=false p. 18
For an already deeply unpopular war, adding an expensive mass mobilization and a commitment to a major land campaign in North America could easily bring down whatever government proposed it.
Also, realistically if the British blockade the U.S. coastline (and thus lose access to U.S. grain exports) then they are pretty much going to have to strip India bare to prevent massive food riots in the British Isles. Remember the British are losing out on 1,753,000 tons of U.S. grain which is keeping 40% of the population of the British Isles alive. There's only going to be so much surplus grain floating around the world market, so the British are almost certainly going to have to resort to mass expropriation of Indian food supplies to make up the difference and prevent mass starvation in Britain. And stealing Indian food supplies is going to mean massive unrest in India. So the British are going to have to keep a large amount of their army stationed in India unless they want to lose the crown jewel of their empire.
Also, would Canada even have the logistical infrastructure necessary to sustain a 400,000 man army in 1881? That's an awful lot of troops for a country that only has 4 million people in it.
The British have another advantage: they have 50% greater manufacturing base. Numbers are good. Weapons and munitions are better. It is going to be easier for them to fight a long modern war.
I agree, but why commit to a major land campaign when you can effectively hobble the U.S. simply by utilizing your vast navy to blockade its coastline and let the Confederates do all the ground fighting.
And have two "Mexicos" instead of one? I have sure that Sam Clemens would have something to say about Blaine's acumen in this matter.
Why would Clemens have a problem with the U.S. establishing a a pro-US regime in the Sierra Madre region? The U.S. strategic position is stronger with a friendly puppet government in control of that territory then with having the Confederates or the Imperial Mexicans controlling it.