I've lived in South London for 30 years. I don't go into London much but I can definitely see how much it's improved over the years. The Northern line is perfectly fine, as are most other underground and overground rail services. Bus services are incredibly good value for money.
ULEZ was a good idea, although I'm not sold on the expansion as it now extends to the bottom of my road which really isn't in London and has really hurt people who could not afford to change their car.
As for Khan, I know plenty of people in city hall who cannot stand him, they think he's a nasty piece of work. He got in primarily because the competition was so poor.