Would be interesting to see if someone can up with something plausible. Here is my two cents worth.
THe UK had a strong fascist/nationalist movement pre-WWII, much like the US and the German-American Bund party. It would all have to hinge on how appealing these English Nazi sympathizers could make nationalism to the general public. If they could whip up some patriotic fervor for the old empire, then they might mobilize a populist support base, sweep parliament in an emotional vote, and get their own candidate for Prime Minister elected.
What I am thinking is that this happens around 1935, with Hilter having become chancellor earlier. Re-shuffle the deck on his inner circle and throw in some new faces; someone who can compliment Hitler's political brilliance with some much need pragmatic thinking, Bismarck style. An olive branch extended by the Hitler government might lend some much needed support to the British fascists. It also softens the public's view of Hitler (Churchill in fact praised Hitler at one time, if memory serves). Now I certainly might be stretching this, but lets say it is successful. Britain's new fascist government now grows more extreme by the day, keeping pace with Germany. A million or more Englishmen see the writing on the wall and flee to Canada, which is still neutral. The government forces the Queen from the throne. The royal family, along with Churchill and other loyalists, also flee to Canada, without officially abdicating.
Long story short, Europe becomes engulfed in a quad-Axis Empire: Italy, Spain (under pressure to align with the Germans and English), Germany, and the UK. A joint UK and German force spread out across the globe to reinforce England's hold on her territories and commonwealths. Pearl Harbor happens about this time, as Japan is timing her conquest in the Pacific with her allies consolidation in Europe. America is pissed, OTL, and Churchill, who is now "Pime Minister-in-exile", is asking FDR to send troops to help the Canadian and British forces. FDR, shifted official recognition to Churchill and his cabinet, alreayd had the troops waiting before he asked. Short of it is that they stop the force from landing in Canada. Bloody and lasts for three months. So there is the US involvement in the war.
Without two fronts and the shift in the timeline, Axis forces never face a bitter Russian winter and take Moscow, with the Japanese pushing from the East. Eventually they catch Stalin moving from one fortified location to the next and kill him, along with the top ranking generals. This fractures the Red Army and turns them into one big guerilla force.
The Australians are doing their best to resist the Germans. This is the first to to get taken back by the Allies (America, Canada, English exiles). It becomes a staging area for a massive push in the Pacific, up into Japan, with a bloody invasion there. They have simply been containing the European side of the Axis, using ever-increasing airpower in the sky to swat them down, but failing to put men on the ground. Shpping in the Atlantic is virtually impossible, so we have been developing our own subs to counteract the u-boats and extending the range of our planes farther and farther. From Japan we exterminate the Japanese forces still centrenched in China and move into Russia, crossing that vast territory.
At the same time, a large English resistance is loosening the fascist hold in the UK and general unrest in destabilizing Nazi hold there. The fascist government is overthrown and a D-Day style re-taking of the UK takes place. Because of his hold on the UK, Hitler never has the Atlantic Wall built. We're able to push troops into Europe with much less effort. Spain puts up something of a fight, but renounces its alliance and declares its neutrality. Italy is too stretched into North Africa and the Middle East and their lines snap. Germany still has the bulk of its forces invested in its fight in Russia and tries to split them. This takes to long and breaks up both fronts. The Allies sqeeze and push hard. The Germans push back, but eventually, there is no more room to push. They surrender.
I know that is simplistic, has a bunch of holes, and needs a lot of tweaking, but it is a down and dirty timeline. What it gets you is this: American troops are already running half the government functions in Australia and New Zealand. There are as many American troops and Canadian troops in Canada and there are a lot of Americans in Britain. There are also British resistance and British forces spread across Asia and Europe. Re-building and introdcuing democracy to these regions is going to take a lot of work. The only country with the resources and existing infrastructure to help the US is the UK. Basically, we rule two third of the world jointly. The UN isn't going to be possible at this point. Unification doesn't seem like such a bad idea.
Anyway, that is a shoot-from-the-hip explanation. Take it for what it is worth.
