In nearly every year for at least 250 years, deaths outnumbered births in London.

From Shakespeare The World as Stage by Bill Bryson.  Chapter 3 page 45.

Few places in history can have been more deadly and desirable at the same time than London in the sixteenth century. Conditions that made life challenging elsewhere were particularly rife in London, where newly arrived sailors and other travelers continually refreshed the city’s stock of infectious maladies.

Plague, virtually always present somewhere in the city, flared murderously every ten years or so. Those who could afford to left the cities at every outbreak. This in large part was the reason for the number of royal palaces just outside London—at Richmond, Greenwich, Hampton Court, and elsewhere. Public performances of all types—in fact all public gatherings except for churchgoing—were also banned within seven miles of London each time the death toll in the city reached forty, and that happened a great deal. 

 

In nearly every year for at least 250 years, deaths outnumbered births in London. Only the steady influx of ambitious provincials and Protestant refugees from the Continent kept the population growing—and grow it did, from fifty thousand in 1500 to four times that number by century’s end. (Such figures are of course estimates.) By the peak years of Elizabeth’s reign, London was one of the great cities of Europe, exceeded in size only by Paris and Naples. In Britain no other place even came close to rivaling it. A single London district like Southwark had more people than Norwich, England’s second city. But survival was ever a struggle. Nowhere in the metropolis did life expectancy exceed thirty-five years, and in some poorer districts it was barely twenty-five. The London that William Shakespeare first encountered was overwhelmingly a youthful place.