For almost the whole 19th century, France and Russia were the natural enemies of Britain,
Russia? Yes. It took three disasters for Russian policy (Crimea, Bulgaria, Manchuria) for us to stop worrying about their Wicked Plan, and that was only because they were no longer in any position to actually implement it.
But France? Our relations with Napoleon III varied between decent (as in, hardly worse than our present relations with Sarko) and intimate. We made sure not to allow France to die out as a great power after the F-P war.
There was a period late in the century when between colonial tensions and the Franco-Russian alliance, we could just about have gone to war if everything had gone wrong at once (see
Fight and be Right), but immediately after Fashoda the honeymoon started and after Tsushima we were getting closer and closer. Once colonial conflicts had blown over and we had lost our fear or Russia, we had every reason to move closer to France, and vice-versa. "Almost the whole"? Nah.
I would agree that a Russian victory in the Far East leaving Japan as a British semi-dependency - plus Franco-Russian allies in the Ottomans and Italy - could at the right date (1915-16, with a reformed Ottoman army, 3-year conscription, and Russian railways) give Germany and Austria a run for their money. Direct British involvement would close the question, but at a stretch you might have Britain become involved at the last minute
And while we're speaking of
Fight and be Right, let's make Britain Unionist to boot. Hardline attitudes to India, Ireland, and socialism. By the 30s, Britain is struggling with internal problems throughout the empire, dealing with unethusiastic dominion, and increasingly dependent on a Germany that has slipped ahead on all fronts. Defeated France is too weak to try anything, but lets its sympathies with the alliance of the United States, the Republic of China, and the Socialist Federal Republic of Russia against the
Weltreich be known. Japanese crackdown against guerillas in Manchuria - No Surrender!, says General Zhang. Another round of Irish bombings - American fuse mechanisms. How were they acquired? The Home Secretary, for one, thinks he knows. Then a Latvian youth with ties to the Russian secret service blows up the Duke of Kurland. We will stand by the forces of international democracy, says the president. Alliances go into action. History repeats...
Behold, my sketchy submission.