'Cause this is regarding the Empire, and not just the UK, I'm curious as to what happens to Canada, Australia, New Zealand and South Africa. I can see particular upheaval in the last one. And overall earlier nationalist sentiment and a drifting away from an over Imperial Britannic identity; it's easy to see yourself as a Canadian rather then a "Britainnic" in Canada if you've been fighting a losing war for the metropole.
I had some thoughts on Australasia on page one.
One big determinant will be how much of Germany's Empire the British keep. If the settlement can be spun as 'the Kaiser has won in Europe, but the world is British,' that will be very different to a negotiated peace where thousands upon thousands of square miles of captured territory are handed back despite the defeat of their garrisons.
South Africa will, I presume, be upset about losing Sudwestafrika. New Zealand and Australia will be seriously pissed about handing back Germany's islands in the Pacific. There is, in fact, probably going to be some politicians who talk about refusing to return them- though I doubt they'd get much traction, it could embarrass the home government.
Australasia
really cared about those islands. Richard Seddon irritated the Germans to no end during Britain's negotiations to withdraw from Samoa. He's gone, but there are plenty of NZ politicians who think that control of Samoa (plus Tonga & Fiji) is vital to the colony's security, growth and prestige.
Alfred Deakin is still about in Australia, and he had become bitterly convinced by 1907 that Britain wouldn't have any territory in the islands if it hadn't been for the courage and persistence of Australasian. To some extent he'd feel that he'd been vindicated in his assessment if the British return Germany's colonies- and he's still very much the elder statesman of Australian politics.
Overall, I think both strains of colonial nationalism would be severely agitated by a defeat in the Great War- the working-class, Labour movement focused, often Irish, street level type that I discussed earlier in the thread; and the more middle class Liberals who believed that the Imperial government wasn't paying sufficient attention to legitimate colonial concerns.
Certainly, I would expect that the Australian Republican movement would come roaring back to life. It had been very strong in the late 1880s and 1890s, and one of the best arguments against it was the need for British protection. If that protection has proven to be hollow, expect to see the virulent nationalism of White Australia regain its ancestral link with republicanism.