I have lived in central London for 25 years and never experienced this, nor do I know anyone who has.
However, I know the problem exists and I have just been lucky. I am not claiming that my experience invalidates that of others - just adding my anecdote to the pile.
I think it partly comes down to what you look like and how you act on the street. Of the people I know who have had their phones snatched the common denominator was usually being too comfortable standing on a street staring at their phones. It's hard to miss kids on bikes/mopeds if you're watching for them, but if you're not and they appear then they'll go for you.
Depends how used to living in a big city you are. I think those of who live here have a bit more situational awareness (that said, the moped thing is new and maybe they roll up so fast situational awareness won't help).
However, I know the problem exists and I have just been lucky. I am not claiming that my experience invalidates that of others - just adding my anecdote to the pile.