The touristy areas thing is probably a big deal. I've also spent ~10 years in London, some of it in Zone 1 without witnessing any attempted street thefts or knowing of any friends being mugged. Approx 1 week in Athens: two, one targeting me (neither successful)
There might be a difference in street crime between London and Athens but it's not that big.
20 years here (in this stint) and I've never seen it but I do tend to avoid crowded places (social anxiety) except when peak travelling.
I do know people who've been moped'd and mugged - never suffered either myself (although I apparently have a "resting hate scowl" according to my sister which scares people away.)
My wife had her phone robbed from her in this way in Canonbury (N5) 2 years ago.
It was very scary for her since they went up onto the curb and pushed her onto the tarmack as they grabbed it. It happened at around 6am in the morning at most 20 metres from our flat which was on a quiet terrace of victorian houses.
It's not just touristy areas. It's probably easier for the motorbike thugs to operate in places which have relatively quiet roads that they can escape on. I suspect that if you live in a nice area, but close to some of the inner city ghettos you are most at risk. I've also seen it happen in and around the parks.
There might be a difference in street crime between London and Athens but it's not that big.