Yes, but I would consider it somewhat rude to use the bell in a space where both bikes and pedestrians are allowed. If it would be required to be used regularly, I'd say the path is badly designed.

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.

Different folks have different preferences.

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.)