I'd just like to call your attention to this fascinating scholarly work on Shakespeare and London (note: not Shakespeare's London or Shakespeare in London). I just finished reading it, and I learned an enormous amount from it. Shakespeare in London relates biographical details of Shakespeare's life, but it connects those to the biographies of others who doubtless surrounded him in London. It also tries to find as many connections between London events or personages and Shakespeare's plays.
I'm providing a few pages of the introduction to give you a feel for the book.
The book then moves on to chapters entitled "Stratford to London," "Places," "People," "Art / Authority," and "Diversity" before bringing the subject to its conclusion.
I highly recommend the book as an endlessly intriguing examination of Shakespeare in London and London in Shakespeare.