I've thought about this myself and although I haven't received my license yet, I'm taking the lessons and a car should be waiting for me by the time I'm 18-19. It is difficult to maintain and commute in London no matter which route you take, driving or public transport. The way I see it, public transport is public and I hate being on a train stuffed with many other people sweating and rubbing against eachother like melting maltesers in a bottle. Public transport is public so school children a few years younger than me will hop on the bus screaming and knocking on everyone's head for a long ride that could be cut down to a few minutes in a car because of all the stops and lack of shortcuts. The only good thing is that it's cheaper, especially when commuting in central London because of all the congestion charges.
It all comes down to whether you're willing to spend thousands and thousands on insurance and maintaining a car in exchange for some privacy and shorter journeys and I would much rather do that.
It's up to you but I just thought I would throw what I think out there.