The premise here is that in the 1930's a larger red scare across Europe leads to much more right-leaning governments in many places, including Great Britain, which goes full-blown fascist in order to "preserve the empire" or something.
The question isn't how it happens, why it happens, or what exactly happens, but what would the goals of such a state be? At this time the British already control the largest empire in the world. What else could they hope to gain? I can't see them expressing any irredentist claims to, say, France, or Hannover, or, god forbid, the USA. I imagine they might reincorporate Ireland if it all occurs after the Home Rule Bill is passed. Were there any areas in the world where the British felt they had missed the boat, so to speak?