I used to commute to work by bike in ~1M city in Europe, mostly on dedicated bike lanes, but some shared, and had just the smallest, barely audible bell, only because it was required by law. I don't remember using it much at all. I don't know what the problem is. Maybe the Londoners should take a good look at themselves.
I agree that on a footpath pedestrians should be treated as having priority.
A semi-common way I use my bell: when on a shared footpath with plenty of space to take over, I often use my bell when I'm still ten meters away, so that I don't give pedestrians are heart attack by suddenly dashing right past them.
(I have a nice ding dong bell. They don't seem to mind. It also helps that I often have a cheerful five year old in the back.)
For example, I can go into datacenter and it will cancel all the datacenter noise(aside for when air blows directly into mic, it overdrives it) but I can still hear what other person is saying.
Also I used them to generally listen to podcast so there was no wall of music to go thru, so sirens and such were easily discernable
If you listen carefully you can usually hear a cyclist behind you who may want to pass or is passing you, and having headphones probably makes that a lot harder
The most problematic people in traffic are never aware that they are the problem.
Safe or not - it is up to individual to decide if it is worth the risk.
I used to live in a city where I would walk everywhere but I had the constant fear of cyclists running over me because they would drive all over the pavements without any regard for pedestrians. Imagine walking and having to look around all the time. I find it amusing how people in websites like this one talk about how we have to be very afraid of cars when the true terror, at least for me, were cyclists.
They are though(at least here in the UK) - a guy was convinced of manslaughter for hitting a pedestrian on a bike just last month. In general the rule is that the person in charge of a bigger/heavier vehicle is the responsible party in almost all collisions.
One large fine, and people will learn.
Jaywalking is even a misdemeanor in some areas of the USA, it doesn't stop it from happening at all.