The poem that Churchill recites, beginning "Who is in charge of the clattering train?", is "Death and his brother sleep" by Edward James Milliken.
Now that I'm in charge of the Navy, Mr. Hitler and his Nazi thugs had better look out. We're going to teach them a lesson that they'll never forget.
The famous speech Churchill wants to revise (and later delivers in the House of Commons) in the beginning of the film ("To see Mr Gandhi, a seductive Mid-Temple Lawyer ... posing as a half-naked fakir in a manner quite well known in the East, striding up the steps of the Vice-Regal palace to parley on equal terms with the representative of the King Emperor") was actually delivered in 1930, whereas the film starts some years later.