I've visited London, and your rail systems (both the Underground and the national rail) are amazing. I feel very strongly that if more Americans could see how rail works in and around London with their own eyes, it would make people realize that it was the right approach for major cities.
I think that in the US, the problem is that most public transit is absolute garbage[1], and so people who have only lived here don't realize that it can actually be superior to a car for commuting if the people are willing to provide the funds to government and insist on using it to build a world-class public transit system. Therefore, public transit rarely improves, and so it's perceived as "the poor person's option" because it's extremely slow compared to driving, and generally absolutely filthy.
[1] To make things worse, the employees of the transit systems seem to generally be told that the systems they're supporting already are "world-class", and "the envy of the country", so they feel like there's no room for improvement.