I'm also a Londoner (Wimbledon) and I think the London Tube map alone would be great, however the reason I decided to focus on central London and include territories is because:
a) there are copyright issues with using the tube map. I know you mentioned changing the names, but the iconography (if that's a word) is the copyright concern, so it'd end up just being lots of made up names linked by lines that happen to be the same as the underground lines.
b) it makes it more interesting to non-Londoners, which is key. People know the names of the central London territories from Monopoly and other references, so it has a worldwide appeal. We're allowed to use real place names, just not the real London tube map (someone attempted it and was shot down by someone from the London Underground, and it ended up looking horrible in my opinion).
c) The tube map is very linear, with lots of places, such as Wimbledon or Amersham, being a point at the end of a line. This doesn't make for very good gameplay.
d) As you mention, the lines themselves will be very difficult to hold as they have so many interchanges and cover most of the map. Adding territories gives players much smaller and more achievable bonuses to hold. I feel if it were just the lines then most games would just end up as a straight effort to kill the other player without holding regions, which would just come down to dice.
e) Most importantly, I think it'd be more fun. I think the idea that territories can only be attacked by tube stations means people have to travel on the tube to get he bonuses. I may end up taking out any bonuses for the lines themselves as they will be extremely difficult to hold. Maybe even have hold the circle line to win, since it is nearly impossible.