Since there were British Fascists, the idea of a Fascist Britain seems legitimate enough - and it's a What If anyway. Perhaps we can discuss the hypothesis without belittling it?
I called his scenario ridiculous becuase it is (Britain stays out of WW1 because... idunno, and the Germny still looses because... idunno, and then the Treaty of Versailles is still signed because... idunno, and then germany still goes Nazi because... idunno, and then the Axis is formed because... idunno, oh, and Russia is communist because... idunno). I called his question silly because he's arguiing about whether Britain is in the "Axis" or the "Allies" as if these are constants that countries shift between (too much HoI2?), whereas any timeline which changes enough to turn Britain fascist does away with both.
You'll note that I speak glowingly of FabR, a timeline which comes close to the idea of "fascist Britain". Nothing is inevitable, after all. I'm not attacking "fascist Britain" under any circumstances ever, only under obviously stupid ones.
Furthermore, the BUF were a sad joke. People think of them when they think of Fascit Britain because they were by their own proud admission fascists, but they had a snowball's chance in hell of taking power. What you need to do is go much further back and establish conditions allowing a "fascist" regime to come to power naturally and plausibly, and it probably won't be called Fascist. This is what FabR does, for Russia too (where the analogous problem is with fascist White emigre organisations).
How about a POD closer to WW2?
Had the Danzig crisis been delayed for whatever reason (local Nazis less strident, Poland more efficient in frustrating the Free City government's call for a union with the Reich, Hitler more cautious), and with the Soviet Union launching operations against Finland, could Hitler and Chamberlain have reached an agreement based upon joint help for Finland and denunciation of the Molotov-Ribbentrop Pact?
The Soviets attacked Finland (and bullied Romania and undermined the Baltics) because of Molotov Ribbentrop and the partition of Poland. Until that's happened, the Soviets won't attack so brazenly.