Comment by connorboyle

You seem to be using vanilla (or one might say "area-weighted" population density numbers. The article specifically says that they are using population-weighted population density numbers for comparison:

> Population weighted density refers to the density multiplied by the actual number of people living in each area, and more closely reflects the density that people experience.

One indication of this is that they give a different value for London's population density (9.2k / km^2) than you do.