American History by British Authors ...

[V.C. Brunswick]

I recall seeing an alternate history-type movie about Britain being part of the Nazi empire. Rutger Hauer was in it, and it took place in about 1964 (there's a scene where he's on a train I think, and passes a billboard advertising the Beatles' first album!). The British government, under Churchill still as I recall, is in exile in Canada, and there's a scene where an American news reporter is asking questions about the odd disappearance of Jewish relatives of American citizens.

Or am I dreaming all of this? Anyone else recall this film?

I believe the film you're thinking of is Fatherland (1994)

"Fatherland" shows a world where Nazi Germany won the Second World War after repulsing the Allied invasion at Normandy. Now, in the 1960s, Germany continues to fight a bitter guerilla war with the Soviet Union and desperately needs an alliance with the United States in order to finally beat Stalin's war machine. However, when local SS-homicide detective Xavier March (Rutger Hauer) begins investigating the mysterious death of a Nazi Party official, a coverup is revealed involving the Jewish Holocaust of World War II. With the assistance of an American journalist, March probes deeper and discovers the full truth about what happened to the Jews; a truth that could destroy the peace process with America and a truth that Nazi and SS leaders will stop at nothing to keep hidden.