Other references in the film include a reference to Puss in Boots, which is in itself (in some versions) a reference to Dick Whittington and his Cat. Dick Whittington was both a real historical figure, Richard Whittington, and a character in the pantomime. The brothel/boarding house are located in Whitechapel.
When Roy and Chon are arrested they are taken to Scotland Yard, and later in the movie they are taken away in a Black Maria, after being arrested in Madame Tussauds. An interesting aside is that Jackie doesn't have a wax figure in the Tussauds in London but does in Paris, Hong Kong, Shanghai and New York. His figure in New York is bright orange for some unfathomable reason.
Roy and Chon have to rescue Queen Victoria from an assassination attempt at her Golden Jubilee Celebration. Ignoring the chronological difficulties, as the real Victoria celebrated her Golden Jubilee on the 20th June 1887 (which was prior to the events in Shanghai Noon even). However there was a real assassination attempt on her at this time, which is known as The Jubilee Plot. The Jubilee Plot was a Fenian (Irish Nationalist) plot to blow up Westminster Abbey, the Queen and half the British Cabinet.