A series of maps to show the areas of London and their populations that are further than 1 km away from a tube station. View them all here
Unsurprisingly, central London is very well connected by the tube. In the City of London and Westminster you are never further than 1 km away from a tube station. In my borough of Islington, there are only 3,500 people who live more than a kilometre from one of it's 15 stations.
The further out you go, the more people there are without easy access to the tube. Bromley has the most, with 248,000 people – though they do have quite a few national rail stations available.
This was all produced in QGIS, with the analysis all being done using the brilliant Graphical Modeler.