Something like this:
The Gallipoli offensive succeeds.
WW I ends in an Allied victory.
Ireland gets united Home Rule as a Dominion. Britain suppresses a Republican uprising using only Irish battalions, then suppresses an Ulster uprising the same way.
Due to the costs of the war and the weakness of the Imperial House (Alexei's illness, Rasputin, etc.), Russia goes viciously fascist, discarding the monarchy. The new dictatorship militarizes the country effectively (Maximum Leader Brutalov is a bastard, but he's a smart bastard).
The victors fall out over the Middle East. France and Russia ally against Britain. Japan breaks with Britain over Pacific ambitions and joins the alliance, becoming hypermilitarist as OTL.
In the Second Great War (1933-1936), the Wheel (France/Russia/Japan) defeats Britain. Japan conquers Malaya, Borneo, and the Pacific, Russia conquers the Middle East and India, France conquers British Africa. France, supported by Russia, and also remilitarized Germany, looking for revenge and a jackal's share, invades and conquers Britain. The US had supported Britain, unites with Canada and Britain's West Indies colonies. Ireland falls to an army of Republican exiles sponsored by the Wheel.
Victorious General La Flamme seizes power and proclaims himself Emperor.
Nuclear weapons invented.
Cold War between the US and the Wheel. Japan breaks with the Wheel, pursuing its own ambitions.
In Great War III (1965), the US and the Wheel largely destroy each other in a nuclear war, Japan remaining neutral.
Afterwards, Japan is the only real power left. Japan reaches out to establish a global network of bases, to keep order and secure its control of whatever resources it wants anywhere. Japanese becomes the language of international affairs, science, and high culture.
Japan props up a puppet Emperor in the ruins of France. Ireland was a Wheel satellite; Dublin, Belfast, and Derry are destroyed by nukes, leaving the untouched Gaeltacht as the surviving majority. General Murphy restores order and proclaims himself Ard Righ.