American in London for 14 years. The mystery has finally broken for me on this topic, quite recently. First let me say that every other answer is completely correct. But, none of them really unravel the mystery of the cultural difference. When I first arrived here, I was alarmed that it seemed pedestrians "yield right-of-way to cars". This is a big misrepresentation. Let us look at history.
Roads were originally for walking, and later, the occasional horse and/or carriages at or close to walking speed. Then, bicycles and motor cars arrived, eventually traveling significantly faster than foot traffic. The crux of London road use is that nothing ever fundamentally changed: all traffic is road traffic and all users are expected to watch out for their own safely and the safety of others. This includes responsibilities of pedestrians as well as responsibilities of vehicle operators.
The UK driving manual even includes a section on the responsibilities of foot traffic. See https://www.gov.uk/guidance/the-highway-code/rules-for-pedestrians-1-to-35
What follows naturally from this is, by stepping into the path of an oncoming car, you have inconvenienced that driver by causing him to slow down - and also making him fear for the possibility of a traumatic collision. Try this with another pedestrian, perhaps at the shopping mall? Turn suddenly and step directly in the path of your neighbour, close enough that they can not be reasonably expected to stop before bumping you. The reaction will be anger. And this is exactly what the London driver feels when you encroach on his otherwise peaceful, non-murderous driving. Legally, he is compelled to stop for you, but it is rude that you have inconvenienced him. In a British face-to-face situation, you would have immediately apologized, and he would have apologized in return to de-escalate the situation.
There is a stark contrast in history with what happened on American roads. The motor cars arrived, became faster, and the legislation followed. They created crosswalks, pedestrian traffic signals, and jaywalking laws to essentially outlaw walking on the road. It's important to note that although various pedestrian crossing systems and refuge structures arrived in the UK road system, none of them replaced the original and natural right to walk in the road. (That only happened when the Motorway was introduced. Pedestrians and certain categories of vehicles and drivers are simply not allowed on the motorway.)
Now if you dear reader have learned something from the above, then read the other answers and comments and you may begin to understand the principles of road use and how they derive from face-to-face conventions.
This is part of a much greater cultural difference: that of rules-based vs. principles-based systems. In American law and accounting, almost everything is rules-based.