When King George VI says, "I'll get her [Princess Elizabeth] to marry a Greek or someone," this is a reference to Elizabeth II's real-life marriage to Prince Philip, Duke of Edinburgh, who was born in Greece as the son of Prince Andrew of Greece and Denmark.
In an outtake of the television series 'Travel Man', Bob Mortimer tells Richard Ayoade that while filming this movie Mortimer convinced lead actor Christian Slater to invest £350 on some technical drawings for Mortimer's idea for a 'reverse toilet'. Perhaps unsurprisingly this idea didn't come to fruition, and Slater lost his initial investment.
The real life Winston Churchill was actually half-American. His mother Jennie Jerome (Lady Randolph Churchill) was born in Brooklyn in 1854. His grandfather, Leonard Jerome was a New York State Assemblyman.
The Adolf Hitler character is mistaken for Charles Chaplin on more than one occasion in this movie. Once by a cab driver and once by the King, Hitler is the subject of mistaken identity joke for Chaplin's the Tramp character from the classic silent comedy The Gold Rush (1925) where he is remembered for eating his shoe. Interestingly, it is of note that Chaplin spoofed and parodied Adolf Hitler in his later movie, The Great Dictator (1940),
On the DVD commentary during the scene where US Churchill and Denzil Eisenhower exit the British War Office: director, Peter Richardson, dubs, "This is very r... relevant to the Iraq War".