This all depends on the timescale we're operating under, of course. When is this war occurring? What leads up to it? Etc.
I'm currently operating under the assumption that there is a rift in US-UK relations in the aftermath of WW1, with the peace treaty against Germany being incredibly harsh, leading to the US denouncing it and withdrawing from the participation in the treaty, nonparticipation in the League of Nations, etc. Wilson himself limps through the rest of his term, devastated at how he has been ignored by the imperial powers of Europe and how the nations of Europe had been divvied up for their game. The US continues its hurried shipbuilding, perhaps even accelerating all that they can (which isn't much) - they are fearful that what happened to Germany might someday happen to them. Some floaters about a conference to end the accelerated construction of large warships, but the calls on both sides are ignored, and the US and UK forge ahead with their construction goals. Considering how US-UK relations have turned sour, the UK and Japan maintain their relationship.
In 1923, the Ruhr is occupied by the French and the Belgians. With animosity greater between both sides of the Atlantic, the eventual Dawes commission does not end up being created, and the occupation of the Ruhr continues for an even longer period of time while the British try and dislodge the French. The Great Kanto Quake strikes, and the majority of Japanese shipbuilding grinds to the halt, taking them out of the race. And, in 1924, the first of the
South Dakotas and
Lexingtons begin to be launched, and the UK is hustling to attempt to build enough N3s to keep up. Seeing that the UK is at risk of losing the naval monopoly, especially now that the Japanese are years behind their building schedules, it would be best to try and risk war now when the UK has a reasonable advantage and with an ally in the Pacific to distract them than to risk war later.
And here, Canada could go and refuse to join in to protect itself, remaining neutral, or it could launch its first strike, but in this scenario both nations have been preparing for war for years. It's not a sneak attack against an unprepared foe.
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Honestly, that's the best I can think of for a war in the time period, as frankly there isn't a reason for the two nations to go to war barring something massive happening in either (or both) countries. I mean... "maybe" the US suddenly goes land crazy and decides to invade Canada? Doubtful. Perhaps the US decides to invade and occupy Canada to protect it from a Communist Britain that is trying to claim the whole Empire for itself? I mean, the whole scenario is such a stretch...
the United States of North America (the South American United States is Brazil)
Pardon? The official name of Brazil is the Federative Republic of Brazil. There is no "United States of South America" or "United States of North America". And why call Brazil that? Argentina and Venezuela are also both federal states with just as much "claim" to the title.
Attempting to diminish the US by intentionally mislabeling it is just petty posturing. I can't recall any other country that has bothered to put America in its name (at least since the demise of the UPCA in 1840).
I would agree that RN forces could blockade and bombard US East and West Coast ports, possibly in alliance with Japan, and probably go as far as seizing Hawai'i, Puerto Rico, Cuba and American Samoa. At a very big pinch, possibly the Cape Hatteras islands, Nantucket, Long Island, Ellis Island and Manhattan. Controlling as it did the 'sea gates' of the oceans, the RN would seize every US merchant ship on the high seas and blockade the rest.
Samoa is lost, same with Puerto Rico, likely. While important, they are vestigial territories whose losses are tolerable.
However, Hawai'i is not nearly so sure as a thing as you're stating. The possibility of the Japanese invading Hawai'i at the peak of their power in 1941 is outright impossible, and that's in the sneak attack. A joint British-Japanese invasion against the fortifications of Hawai'i, and likely a prepared army and navy defense (as, again, the war does not erupt out of nothing).
Here are a list of historical forts and batteries around
just Pearl Harbor. I've taken the time to bold the relevant batteries that would be available for defense, and that's not assuming butterflies in the timeline eventually leading to
further defenses being set up.
The Harbor Defenses of Pearl Harbor, Hawaii
FORT BARRETTE / Kapolei /1934- / city / county park / KKK
Hatch / 2/-16″/ BCLRN / 1934-1948 / casemated-WWII
FORT WEAVER / Puuloa / 1899 (1922) / Navy Housing / K
Williston / 2-16″/ BCLRA / 1924-1948/ ARF, destroyed
AMTB No. 1 / 2-90 mm/ F / 1943-1945
Weaver / 4-155 mm / PM
FORT KAMEHAMEHA / Queen Emma Point / 1908-1949 / Hickam AFB / MD?, MC / KKK
Hasbrouck / 8-12″/ M/ 1914-1943
Closson / 2-12″/ BCLR / 1924-1948/ casemated 1942
Selfridge/ 2-12″/ DC/ 1913-1945
Jackson/ 2-6″/ DC/ 1913-1943
Ahua/ 3-5″/ NP 1942-1944/ Ahua Pt.
Barri/ 2-4.7″/ A-CM/ 1915-1924/ Bishop Pt., destroyed
Chandler/ 2-3″/ P-CM/ 1915-1942/ Bishop Pt., destroyed
Hawkins/ 2-3″/ P/ 1914-1943
AMTB No. 2/ 2-90 mm/ F/ 1943-1946
Kam/ 4-155 mm/ PM
Puu O Hulu M.R. KK
“Hulu”/ 2-7″/ NCM/ 1942-1944 / incorperated into BCN# 303
#303/ 2-6″/ SBC/ 1942 NC/ tunneled into rock
Other locations- Pearl Harbor ?
Arizona/ 3-14″/ NT/ 1945 NC/ Kahe Pt., from USS Arizona
Burgess/ 4-8″/ 2xNT/ 1942-1948 / (Salt Lake) near Aliamanu Crater, destroyed
Brown’s Camp/ 4-8″/ RY/ 1937-1944/ Browns Camp, Kahe Point
Adair / 2-6″/ A-CM/ 1917-1925/ Ford Island, empl. elsewhere earlier ?
Boyd/ 2-6″/ A-CM / 1917-1925/ Ford Island
“Homestead”/ 3-7″/ NP/ 1942 / Keaau Homesteads
Nanakuli / 2-5″ / NP / 1941-1943 / plus 1 – 3″ NP / destroyed
Oneula/ 2-5″/ NP/ 1942-1944/ Oneula Beach (Ewa)
unnamed/ 2-240 mm/ H 1931-1941/ Laie
unnamed/ 1-240 mm/ H 1927-1941/ Pupukea
unnamed/ 3-240 mm/ H 1930-1941/ Makua
Awanui/ 4-155 mm/ PM 1942-1944/ Brown’s Camp
Barber’s Point/ 4-155 mm/ PM/ 1937-1942/ Barber’s Point / destroyed
X-Ray/ 4-155 mm/ PM 1942-1944/ Oneula Beach / destroyed
Homestead/ 4-155 mm/ PM/ 1942-1944/ Makua Military Reservation
Kahe Point/ 4-155 mm/ PM/ 1942-1944/ Kahe Point
There are other batteries available. Just thought I'd make the point.
Let's not even forget the range issue. It's thousands of nautical miles to the nearest Japanese or British base of any significance; British forces simply do not have the range to bring more than their largest ships. The yellow line is the mark for 2500 nautical miles (the Queen Elizabeth and the Revenge class had a max range of 5000 nm) and the red line is the mark for 2750 nm from Pearl (Nagato's max range was 5500 nm). It's impossible for the British to bring any of their more modern ships to try and invade the most important US naval base in the Pacific without risking losing the ships from
running out of fuel.
The only ones that could be brought would be either the
Kongos from Japan or the older
Iron Duke (or older battleships). Perhaps
Hood could have reached there, but it'd been pushing it. The worst thing is that the British and Japanese interdict forces coming from the US to reinforce Hawai'i, as the only base from which they could was in Vancouver, which is going to be under heavy assault at the least.
So, no, the Philippines might fall, Samoa likely will, and so will Guam at this stage. But forcing a landing on Hawai'i, at the very furthest reaches of their supplies and reach, against an entrenched opponent with a significant number of fortifications and a large army to resist, all the while having no ability to interdict support except by being on site, burning away precious fuel? It's not going to happen. The Japanese couldn't have pulled it off in WW2 in the best of situations. The two combined couldn't do it two decades before.
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As for occupying portions of the west coast? Again, there's the range issue - the UK can only supply so many ships out of its ports, and has to maintain forces worldwide for other purposes. To look at the numbers... from 1900 to the mid 1920s, the UK built 512 destroyers (and lost 64 in WW1, but i'm not sure how many of those were pre-1900 DDs). That is the E-class all the way to the V & W class and the
Shakespeare class. Of those, 184 designed before WW1, 235 were under construction starting from 1914 to 1916, and the remaining 93 were built from 1917 onwards.
In comparison, the US built 267 DDs in a span of 5 years, from 1917-1922. These were also, nearly universally, longer-legged than the British destroyers. This gives the US a large fleet of destroyers and torpedo boats which can operate locally and harass British vessels, while the British have to deal with supply issues. The destroyers have plenty of range to operate from Bermuda, Jamaica, Halifax, etc, but there is the question if there are enough docks in the Caribbean to support a fleet that would be able to combat the US on equivalent numbers - especially while some ports are under siege. (Halifax in particular).
Any lodgements that do occur must be constantly maintained by sea lines, else risking being thrown back. Such lodgements are far more precarious with Naval support being less than it would be in Europe proper, and attempts to knock them back into the sea would need the navy to support them. Which means that whenever the US Navy attempts an assault which forces the British to divert resources, they would be without cover and be subject to entrapment by local forces, which would be far larger. Such a scenario seems destined to end up in a Dunkirk-style setup, with local forces being far larger than what could be supported from the sea, and Naval support being rather fleeting.
And, while not as heavily fortified as Oahu, the Eastern Seaboard historically had a large number of coastal defenses set up along it. Fort Hamilton alone had 6 12" guns and 8 12" mortars in the relevant time period; by 1927, New York, Boston, and Hawai'i had 2 16"/50 guns apiece mounted and in service (these are the ones purpose-ordered for the army, and not surplus guns from the cancellation of
Lexington and
South Dakota). Combine that support with local fire support from the US fleet, and it's hard to see any significant landings from succeeding. Gallipoli might not be the most accurate specter to invoke, but it's the closest one of that time period, and the US are far stronger relative the the Ottomans and can devote far more troops (simultaneously, the UK would be using their best units instead of second-rate battleships and other obsolescent ones).
The Japanese also historically managed to seize minor portions of Alaska in WW2. If the UK could also hold onto a port on the west coast then things might be more interesting.
There's a slight difference between a few small, and in the end inconsequential islands in the Aleutians and a major port, of course. One of the islands was evacuated beforehand, and Kiska had 10 men and a single dog to offer resistance to an armed landing. I mean, the Moroccans managed to temporarily seize a Spanish island in 2002, but it helped that the island was barren and uninhabited.
If UK and the Japanese can cut US seaborne traffic to Alaska and the U.S. cant push a land route thru via BC
They could also push a land route through Alberta into northern BC worst to worst. Considering how sparsely populated Canada is, the Plains Provinces are a sure loss in the event of a war. And, even then, the Canadians might hold Vancouver, but that would leave the interior wide open.
I could see the Soviets deciding it was a good time to take Alaska
With what Navy in particular? Or are the Japanese providing sea lift? And, considering Soviet success against Poland, a nation that was as connected as closely to their metropole as there ever would be, engaging in a trans-Pacific invasion starting from the most far-flung reaches of their empire is a sure plan to continue those successes.
Then perhaps the UK might try and push further south.
The British invading into Washington and Oregon through... Vancouver? Again, how are they reaching that? Without drawing the soviets in, their nearest base would be Yokosuka, I think. And even then, the closest after that would be Vladivostok.
The disparity of forces are going to be massive by this point in time... I can't help but wonder how many troop transports would get sunk below the ocean TTL as well.
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tl;dr: The US in North America and Hawai'i will prove to be virtually unassailable absent a surprise invasion of a nation that was not expecting war at all, which is an unlikely scenario. The British will successfully manage to take the far-flung portions of the US possessions, and will manage to commandeer or destroy a large portion of the American merchant marine thanks to the numerous bases around the world, but will have difficulty maintaining local numerical superiority at sea even assuming OTL numbers. If we assume that the US maintains its building programs at a constant clip from the end of WW1, then that numerical superiority will certainly be lost.