In a town centre near me they dropped all the kerbs, paved the roads in blockwork, and there are no white lines. Give way signs have disappeared and there is only one traffic light controlled pedestrian crossing point in the blockwork area. At crossroads, they've put circles in the blockwork that look a bit like roundabouts but nobody's sure if they're just decorative or now because there are no roundabout signs.
Cue the local newspapers bleating "oh people will die, people will be hurt... good god think of the children!!".
Result? Well it's been like that for 2 years and nobodies died. In fact, cars all stop at the points where two roads meet because nobody's sure who has priority. It works perfectly.
I think it proves there is an excellent case for paving most of London in pretend roundabouts and roads with no obvious priority. People would soon get used to it, and they'd save a bloody fortune switching off the ridiculous numbers of unnecessary traffic lights all over the city. The dutch are already used to it and that's why it already works so well, but there's no reason why we couldn't be in this country as well.