I don’t know for London, I wouldn’t describe Tokyo as full of cars.

There are major axes to accross the city with constant traffic and most bigger blocks are accessible by car (even just for deliveries). But there are pretty large areas with no car entry, and small residential parts are often shared car/bike/pedestrian zones were cars are not privileged.

I also think the goal shouldn’t be car-free, but to have clear separation of the “liveable” space with shops, parks, administrations, schools etc., and the “transportation” space with the trains, cars, cans and trucks. Speaking of Tokyo it often layers the two, with lower level streets/buses/truck roads and upper level walkable space. Seems to be the best compromise, albeit more expensive to build.