If you are a cockney, you are a Londoner, but if you are a Londoner, you do not have to be a cockney.
Person 2: "I live in Ealing, so yeah I am. Are you?"
Person 1: "I live on the outskirts, techinally in Hertfordshire but I would say I'm a Londoner."
Person 2: "No. No you're not."
"Nah. I'm a Londoner. Move to Hertfordshire when I was 13 though"
Londoner: GIME UR FONE!!!!
Me: Yeah ok stfu you n00b
*uzi's londoner into next week*