Pedestrians do need better provision and a higher priority than currently at most junctions/roads in London - with the caveat that if they push to cross and then cross on red man or wander off, that the lights switch back to road priority.

Stopping all the traffic for 20 seconds to allow pedestrians to cross in all directions wouldn't bring traffic to a halt entirely. They manage to do it at Stockwell gyratory which is a main traffic thoroughfare too.

Traffic in London doesn't move all that fast anyhow - it is a series of short spurts to stop at lights in any case. Making a few of those lights take a little longer - or more of the roads to have a 20mph limit to make them safer for pedestrians (and cyclists) wouldn't really massively impact motorised journey times since the average speed is only something like 12mph anyhow!