1939 was during the War period not before. Immigrating out of German started in the early 1930s. Nazis were in power in the 1920s, not fully. It was around 1928 they started the Culture Wars against ideas and works they deemed Modern, like Jazz. As the book states, the UK was pushing for them to immigrate there instead of their main Island because of antisemitic views. [1] [2]
The author actually traveled and talked to number of celebrities that lived during that time period. Even asking the Nazi era actors if they thought their careers would of took off if fascism never took hold and removed their competition.
[0] https://en.wikipedia.org/wiki/List_of_countries_that_have_ga...
[1] https://www.ourmigrationstory.org.uk/oms/jewish-refuge-and-t...