To be fair there's no reason to believe that what I tend to dub the 'King's Party' (aka Edward VIII, Winston S. Churchill and Oswald Mosley) are working any more smoothly than one might expect - after all we only hear about their Government via radio broadcasts which are unlikely to be based on insider information!
With that in mind it is reasonable to imagine that the working relationship between the Tories and the New Party 'Silver Shirts' degenerates over time - if I were to suggest a plausible reason that it never entirely disintegrates then it would be that Mosley new QUITE gets all his ducks in the row for a coup and simply loses his nerve when contemplating the uncertainty of his success in such an endeavour Vs the certainty of retaining a considerable degree of power and influence as 'Deputy Prime Minister' (for one thing Labour might well be willing to team up with the Tories to scotch Mosley should he get too uppity, if nothing else).
Especially if he were to secure a particularly sharp hook with which to make it very inconvenient for Churchill to show too much resistance.
https://www.alternatehistory.com/discussion/showpost.php?p=11045087&postcount=1430
^At the other end of the link which I have taken the liberty of posting, I posit that between the Wars the British Government would have been very foolish not to reach out to the US Government in the interests of creating an agreement establishing a 'Special Relationship' between the US and the UK equivalent to (but less Mephistophelean than) the Molotov-Ribbentrop Pact.
The two major problems with this happy inspiration would be that the Politician most likely to be spearheading this initiative is Winston S. Churchill (vulnerable to accusations and insinuations which might deal a fatal blow to The Kings Party by virtue of his own half-American heritage) and the fact that there would be significant power blocs in both countries which would require considerable finessing to 'Sell' on the whole business.
The sort of PR Operation that is difficult to pull off if, say, some little worm were to be fed information by a Snake at a crucial point in the delicate process of negotiations (if this information were to balance out plans for an Internal Coup by Mosley, I could imagine the Kings Party deciding to muddle along for just long enough to recognise a golden opportunity to sink Domestic Rivalries beneath a flood of popular enthusiasm for a Foreign War).
I hope that I have given some idea of how a Churchill-Mosley alignment might last JUST long enough to help trigger the Second Great War (basically each one would REALLY like to get rid of one another, but can't quite afford to); One would like to imagine that as the UK is obliged to acknowledge the defeat brought about in part by the Churchill-Mosley antipathy, Winston would publicly broadcast his acceptance of the Vote of No Confidence quite possibly being used to legitimate a behind-the-scenes coup by the Opposition (so that he might obliterate Mosley's chances of retaining any legitimacy) and then proudly obliging his would-be captors to consign him to the ranks of those 'Shot while resisting Arrest' for the very simple reason that "We will NEVER surrender" he said "and we REALLY meant it!" (bonus point if Winston is expressing his defiance with a Tommy Gun in addition to the memory of soaring Rhetoric).
