Churchill: The Hollywood Years was a production of the English film industry.
This movie is less how Americans remember the WWII and more how the English think Americans remember WWII. The jokes are also geared to a specific subset of the English that find Harry Enfield and testicle jokes funny. That is not to say the movie is not going to make you laugh. However…
… you are only going to laugh at the historical inaccuracies. But that’s okay, those inaccuracies are mostly intentional. The movie seems to take place in 1939, which makes some jokes… questionable.