But you put together a pretty good argument that people sending children to school inside ULEZ have come to terms with it and therefore wouldn't be concerned with driving their children to school.
Nope - all I said was that people inside the ULEZ (if they owned cars) would mostly have compliant cars and would have known them to be compliant once the ULEZ was brought in. So I doubt that much of the effect was down to people no longer being able/able to afford to drive their kids to school due to a non-compliant car.
That doesn't cover the 'nudge' factor for ULEZ - a societal push that we should be driving less and getting around more by foot or on a bike.
Nor the pollution effect - fewer cars and in particular fewer of the cars spewing the most pollution makes walking or cycling more pleasant.
Nor the notion that schools used the introduction of ULEZ as a strong trigger for walk/cycle to school initiatives.
All these together meant that walking/cycling became more pleasant and more acceptable and driving more unacceptable regardless of whether the parental car was compliant (which it probably was). Hence a shift towards people walking/cycling to school.