At least this study [1] suggests a mild improvement but interestingly replacing one pollutant with another (due to diesel exemptions).
In my opinion, we should primary focus on improving the standards of public transport. Safety, cleanliness, punctuality and price. I'm a car owner living 15mins drive from downtown of a European capital city, and I refuse to drive near the city because the parking is expensive, there's always roadworks but primarily the public transport is excellent and comfortable.
[1] https://www.sciencedirect.com/science/article/abs/pii/S01660...