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They're actually a bit more open than that. They do say that they're all for the idealized "proper woman," but their pitch to working-class men also includes restoration of control over the family. Amid the "angel in the house" rhetoric is an explicitly supremacist ideology, and many of the party's thinkers and orators don't bother to mask it.
The party's attitude toward women mirrors its attitude toward colonial peoples - sure, everyone exploits their colonies, but the Imperials shed the white man's burden/mission civilisatrice rhetoric and portray imperial supremacy and colonial exploitation as ends in themselves.

Oh, for the love of Benji...
As Fascists go they are pretty half-baked then. Any decent repressive regime knows how to get a lot of women onside, even when they are among the designated targets. But that takes time.
What seemed like a "bolt from the blue" to me was not so much that the British might go for a binge of righteous repression and global rampage, but the whole sexist thing. Especially now that you tell us how raw it is. There had to be a buildup to this kind of thing. Well, you've shown us the positives that a backlash could build against, and that's had some long years to fester even before the war started. Then the war must have mobilized hundreds of thousands, maybe millions, of women into all sorts of positions they hadn't been seen much in before, then the postwar years, the years of fumbling attempts to deal with the crash...It's just that I'm left to my imagination for now just how this much high-test misogyny could brew up; what British society might have been like just before the crash.
A more subtle reaction would still be bitter but might go down a bit smoother. As things are, millions of British women--wives, mothers, girlfriends, sisters, daughters--know men who voted in a government whose platform is they can no more be trusted than a bunch of heathen savages, and have the same value. That's got to be a poisonous memory for generations to come.
Also--the IP is indeed half-baked. They haven't got enough women onside to start with. They surely have some; there's always subservient women, and "Ladies Against Women"--but these movements get a lot of their reach and punch from mobilizing more women than that...It's sort of the reverse of what impressed me so much about West African Islam in general, and the radicalized Abacarist version in particular, going viral by spreading via the women, as teachers and as mothers.
Clearly they can't be "blamed" for being unfinished; they are shooting from the hip. But they haven't got their act together; they have made unkeepable promises and haven't really shored up their infrastructure against the backlash of disillusionment. That will only come after years of trial and spectacular error.
For the sake of my general Anglophilia I like to think there are a lot of people who thought this was wrong from the get-go and said so right away and vigorously. After all, even though the IP did win an actual majority, that was of a somewhat limited franchise--only a few women allowed to vote against them, and it could be the men of the British working classes weren't entirely enfranchised yet.
{in answer to my saying "win by extorting it from the colonized" wouldn't work...}
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No, of course it isn't. But it superficially sounds like it should, and in an environment where the economy has gone to hell and the traditional parties have failed to solve the problem, it's the kind of quick fix that some voters will find appealing. Especially since the Imperials have been busily blaming the empire for the economy going to hell in the first place.
(You mentioned below that the takeover seems to have happened like a bolt out of the blue. Things do happen that fast sometimes in a crisis environment - in 1928, the Nazis were a joke, but by 1934 they held absolute power. But maybe I should backtrack to 1913-14 and show a narrative scene on the ground in the UK, either before or after the dominion update. Or... well, you'll see when I decide.)
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Oh, I never doubted that it would make sense and can even fill in some blanks myself, though I daresay your version would be the more satisfying! The misogyny angle, and the sheer concentrated venom of stupidity in general, was the surprising part--rather than seeing the mainstream parties fumble themselves into the ground until the pressure built up like this, I rather thought (since you warned us bad times were ahead, or I'd have hoped for better) that the ruling classes would muddle along without the spectacular depths of failure, running themselves into the ground but at a more majestic pace, with these sorts of developments happening all right but gradually, in an escalation.
That would be less shocking day to day, but perhaps over time and cumulatively, worse. This way these Imperialists will make spectacular asses of themselves in very short order--doing a lot of damage as they do so, but not leaving behind much of a legacy latter-day bigots would want to rally to.
If a Red Britain is the outcome, it too might be rather sadly dystopian and doctrinaire; to an extent bitter reaction against the slanders and injuries of the Imperialists, and to an extent a reconstruction of some of their own--ideas, and people, because no matter how much I want to amplify the opposition at the end of the day a lot of British men did vote for this. Having burned all their bridges to a friendly and comfortable
menage with colonized West Africa, India, and God knows which other small colonies (if only by example) and having proven that mobilizing all the bigots in Britain does not make for an adequate conquest army against desperate and offended peoples who outnumber them by large proportions, particularly when half of one's own metropolitan population has just been kicked in the teeth but not properly tied down first, Britain will wind up terribly isolated, even if the Dominions do remain more or less affiliated. And I doubt very much South Africa can! And Canada and Australasia, even if they won't let Britain be quite alone in the world and more or less support the motherland's flailings, still will have to become
de facto independent, just to manage their own affairs responsibly and sensibly.
I can be more optimistic about a Socialist Britain remaking herself and charming her way back into reasonable relations with the former colonies and in this sort of world I don't have to dismiss the hopes as groundless. But it could easily become a bitter, impoverished communism of shared scarcity--if not so much a North Korea, perhaps anyway an East Germany.
For one thing it might be whiter than it has been up to this point--before they go down the Imperials might make life very hard for the African and Indian origined folks who settled; some might die, others might run. They could go to France; they could return to Africa (to fight for its liberation or afterward) or even emigrate. Even the USA might take in a lot of them--having just acquired still more formerly British colonial islands in the Atlantic.
Black London is older than anyone typically remembers it; substantial numbers of African people were already in England in Queen Elizabeth Ist day. The Africans tend to blend in to the lower classes--meaning that even OTL as here--more British people have African blood in them.
So, despite the fact that the presence of people of color in Britain always seems so odd and so modern, driving them out will be a drastic diversion from the actual steady state, aside from the human drama of it all.
...Americans down south could get some ideas. But I would be very surprised if both don't initially enter the War.
But don't forget, the timing overlaps the period where the Americans who think a bit like the Imperial Party have indeed gotten greedy--and are busy with the Mexican Misadventure!
That doesn't guarantee that no yahoo suggests doubling down, north and south, but such people will draw the looks they deserve.
