Sure, but who counts as "white" changes at their whim. Italians & Irish weren't considered "white" in the United States for a long time. I mean, hell, we're talking about a country that that *Hitler* got his ideas on eugenics from. The US would reinstate its "One Drop Rule" in a heartbeat.
And when it comes to Britain, the fascists here would absolutely include white people in their remigration fantasies considering how much they hate Polish and Eastern European people.
This is probably because white immigration was less of a contributing factor to the UK population in recent history than it has been in America. There is certainly a distinct hierarchy of racism/xenophobia in both countries, though.