The Axis and Allies really can't "ally", even if they're both at war with the Soviets. My suspicion is that at some point, the UK will still declare war on Germany, if Germany's threat ends up increasing over time.
Getting the UK to elect a similar ideology party by 1940 would be fairly tough (I may have to try that), since you can't raise the organization of the monarchists that are already present. Coups against faction leaders are not possible, so it would have to be done via elections. Worse, the thought of fighting the UK later, after they've enacted all of the economic laws as a dictatorship, is scary.