Guess I'm a bit out of touch with young drivers insurance costs
...In my early years i only rode motorbikes and despite passing both my car and full motorcycle tests at 17 i never got round to insureing my own car until i was in my Mid twenties...
Looks like the OP is going to be shelling out more for insurance than a car though!
Personally If i was an 18yr old living in London I'd just forget about a car until i was older...it's not like public transport is an issue in London.
come to think of it I probably wouldn't bother with a car now if i lived in London. adding up the cost of both the car and insurance it would be cheaper to just use Taxi's.