The Elephant was the London public inn at which William Shakespeare and many members of his acting troupe stayed in at least 1599. Dolly Bailey, who seemed to be on sexually intimate terms with the Bard, was one of its employees. Lilith was an apparent subordinate of Bailey, though in reality she had taken the job only as a way to gain proximity to Shakespeare in order to make him change certain words in Love's Labour's Won so that the Carrionites could take over the world.
The Tenth Doctor and Martha also lodged there for at least an evening. That night was important to defining the nature of the relationship between Martha and the Doctor. Though they slept in the same bed, he rebuffed her clear sexual advances in a way that was more plain than when they first started travelling together. (TV: The Shakespeare Code)