The Great European War was brutal. By the end, the warring nations were worn down and exhausted to the point where widespread revolution rocked the continent. Of course the warring nations could not allow this to succeed - after millions of deaths butchering each other in the trenches, the republics, kingdoms, and empires of Europe now found themselves quickly joining arms to suppress the challenge to the old order. The reactionary stage of the war was even more brutal than the previous stage - the fight shifted from clearly defined frontlines to a messy patchwork of uprisings and mutinies scattershot across the cities and countryside of the continent, hitting civilians hard, while the militaries of the established powers saw hemorrhaging losses across the board due to defections. But one by one, the revolutionary territories were beaten down, and subjected to savage slaughter that bathed the streets and countryside in the blood of the radical, the reformer, the revolutionary, the trade unionist, the protester and the mutineer.
The United Kingdom was one of the few areas where revolutionaries were able to gain a solid foothold, with the benefits of the Islands' geographic separation from the mainland, as well as quick victories in Britain with the seizure of London and key ports before loyalist troops could be ferried back from the mainland, a very successful naval mutiny, and a mixture of colonial revolts and the effective alliance-building between various revolutionary, political reform, labour, and protest groups, both within the colonies and the integrated regions outside of Europe. These factors really allowed the British Revolution to be more like a swift coup and seizure of institutional power in many areas, as opposed to the grinding civil war in mainland Europe.
With the revolutionaries on the mainland finally suppressed, the reactionary powers turned their eyes to killing off the last stronghold of revolution and ending the "British abomination". But their "final crusade" was only able to capture a few relatively minor regions before it came to a halt - a second wave of uprisings struck the European mainland. While the first wave demanded radical political and societal change, the second wave was largely devoid of ideology and fueled by mere desperation - years of total war, followed by the revolutionary and counterrevolutionary devastation of cities and countryside had taken their toll, and famine spread across Europe. The uprisings this time saw the involvement of even hardcore reactionaries, simply demanding food and other basic necessities, and seeking to secure such resources (even if it meant fighting among each other) when such demands were not met. So the mainland European powers, crippled by this latest rising, reluctantly turned away from Britain, bringing their troops back home to restore order once more and then return to the factories and fields, shifting away from the "total war" economy and relieving some burden from the masses.
Since then, an uneasy peace fell.
Domestically, the ramshackle coalition of British revolutionaries faced opposition both from traditionalists and secessionists, but were ultimately able to retain control. Britain's peculiar history with democracy is often seen as aiding in the unity of the far-flung territories. Even during the era of bourgeoise democracy, as far back as the mid-to-late 1700s, the British took the unusual step of responding to colonial unrest by simply expanding Parliamentary suffrage to areas settled by Europeans, and then after the slaver uprisings in British North America in the early-to-mid 1800s, a political trend emerged of expanding suffrage and civil rights to nonwhite persons in the European-settled regions, as well as, albeit more slowly, expanding suffrage and civil rights even in the nonwhite-majority territories. So Britain already had some experience with multicontinental integration, and bringing people into the system who once never would have been seen as truly "British". And those dissatisfied with the colonial rule in the territories which saw less integration by the time of the revolution tended to align broadly with revolutionary ideals themselves, and often feared what might happen if they just went their own way rather than bought into the push for accelerated integration by the new revolutionary Britain. The revolutionaries were, after all, despised by pretty much every other government, and non-European revolutionaries were
especially despised, so the fear of conquest by a reactionary power hung heavy in the air. This allowed for at least reluctant acceptance of the project of the multicontinental revolutionary union rather than fragmentation.
In the realm of foreign policy, Britain was initially quite loathed and isolated on the world stage. Indeed, the powers of mainland Europe would repeatedly consider forming another pact and attacking Britain again, though economic issues and squabbles among them would get in the way during the 20s and 30s, and such ideas were largely shelved when Britain developed and demonstrated the atom bomb in the early 40s. As the 20th century progressed, the international situation improved somewhat with various countries taking a stance of cautious neutrality, and in South America in particular, several outright friendly governments emerged, though Britain remains on the whole something of a pariah
A bigger version of the map in the infobox is here
(Yes, borders are pretty convergent considering a POD in the 1700s, I just can't be bothered to be creative and come up with different and original ones. Also, while a WWI basically happened, it went rather differently, with different alliances and motivations, compared to OTL, and isn't just a direct copy of our WWI just with a more powerful Britain)