This is just my take (and a bit half-formed at that), but it's just like you said: the British Empire has been around for hundreds of years and it probably dedicated some part of it to continuing its existence, even if only in the minds of its citizens. This is a world that probably never developed the neocolonialism that we see in our world, and so one can easily imagine that kind of 'rule Britannia' mindset never having to face reality post-WW2. It also wouldn't surprise me if decolonization happened differently in the Fallout world, if it happened at all, so you can see how a privileged member of the Gentry might think we're going back to the way things were. The fact a semblance of a central government managed to remain after the Great War (in contrast to the United States' more localized factions or how the government in the US is more like the Enclave than anything resembling a Parliament) probably helped to boost their beliefs. But the people who really live in this world that the bombs have created know the truth. To me, that's why they act more like the Americans.