London is one the safest city I've lived in (along with Beijing). Chicago and San Francisco are the most unsafe cities I've lived in. People often don't realize this there, it's just that they have been desensitized to it.
I've seen countless accidents in the US, people getting bullied or mugged, cars getting broken in, homeless people everywhere (sometimes shooting themselves up with syringes). Walking in the streets at night can be really dangerous. Most people avoid public transport here and take uber.
On the other side you have London. You'd see single girls walking alone in the streets at 4am. Everyone takes the public transport, never seen anyone fight, almost no homeless people, everybody loves the cops. It's a different world.