-U.K. and France are not allied
-The United States is not involved militarily
-This war would occur after WWII, or at least a World War II comparable to OTL (Germany vs. Soviet Union and any Western powers)
-The Soviet Union should be relatively similar to OTL
Given these circumstances, how can a war develop between the Soviet Union and the U.K. or France. This war should be a somewhat isolated conflict, meaning France is not involved if the U.K. is at war and vice-versa. I think this alone would break the plausibility of the scenario. The U.S. can offer support diplomatically and through aid, but must not formally be at war.
Either power can be allied with any other countries but not each other and the U.S.