I am not sure if it is meant to be topographical or give some sort of
relation of proximities. If you are trying to give somesort of idea of
distance between stations etc, the distance between Uxbridge and the
Piccadilly line at Heathrow seems too great

This is not a topographical map - this is a diagram (which I tried to
make more "lifelike"). The center and parts around Hammersmith and
Whitechapel are enlarged, the border areas are skewed.