Nearly half of Londoners don't own a car and a lot of people who grew up in London don't have a driving license. It just doesn't make sense to drive in central London - it's slower than a bike or the tube, there's an £11.50 ($15) daily charge just to drive into town and parking costs a fortune.
I suspect that most Americans with an injured leg would travel by car unless they had absolutely no alternative, while a lot of Londoners see nothing wrong with hobbling about on crutches.