Dr John Monro was a real person. He was in charge of Bethlem Hospital (popularly known as "Bedlam", from which we get the term for chaos) from 1749-1791. He did indeed believe in cold bathing as a treatment for lunatics.
It's generally believed that King George's first episode of "madness" occurred in 1765, a few years into his marriage with Charlotte. A longer episode occurred in 1788. In 1810, George, nearly blind with cataracts and in pain from rheumatism, went into a deep melancholy upon the death of his youngest daughter. His relapse into episodes of "madness," lead to the Regency Act 1811. His eldest son Prince of Wales (later George IV) acted as regent for the remainder of the King's life. In modern times, the cause of King George's "madness" is thought to be either bipolar disorder or the blood disease porphyria.
In the first scene after the credits, the song playing is a classical rendition of Beyoncé's "Run the World (Girls)." The song is from Beyoncé's album "4,".