When you say "historical background" I am thinking you are asking about the sources which inspired Shakespeare to write Romeo and Juliet. There are several. In 1562, the British poet Arthur Brooke wrote The Tragicall Historye of Romeus and Juliet. There was also a very popular play written by William Painter sometime before 1580. It was part of a collection called The Palace of Pleasure and it contained a similar theme. However, it is likely that all three men (Shakespeare, Brooke and Painter) were familiar with the Italian tales that focus on the theme of young star crossed lovers. These sources include a 1554 novella called: Giulieta e Romeo by Matteo Bandello; a short short entitled Il Novellio, written in 1554 by Matteo Bandello; and A Story Newly Found of Two Noble Lovers by Luigi da Porto, published in 1530.
When an outbreak of the plague struck London in January, 1593, all the theatres, especially those on the left bank of the Thames, were closed. When the theatres were re-opened late in 1594, one of the plays that was probably performed then was Romeo and Juliet. Curiously enough, it played at The Theatre, which was owned by Shakespeare and his partners, known as the Lord Chamberlain's Men.
It is believed that Richard Burbage, a favorite of Shakespeare's, played Romeo. At the time, he would have been 20 years old, somewhat older than Romeo. Master Robert Goff was one of the young men in the company who were frequently cast as young women because their voices were female in tone. It is noteworthy that women did not have frequent roles until the reign of Charles II, who was having an affair with Nell Gwynn, an actress.
The portrayal of the casting for Romeo and Juliet in Shakespeare in Love is very accurate, as is its depiction of a performance of the play. However, the Queen probably would not go to "hear a play" in London, since she could have the plays performed for her at court, a scene which also appears in the film.