A very interesting one.
I very much feel like a Londoner, but my father's family came to Greenwich from a) Kent and b) Essex and c) Rutland in the 19th Century; whilst my mother's family were a) Belgian and b) East Londoners.
My mother, the half Belgian one, felt a Londoner because she lived, as her family had before her for at least forty years, in poverty in East London - she'd EARNED her place, so to speak.
My father, with his generally South of the River ancestry, always felt like a North East Londoner because he was born in Walthamstow E17.
I relocated with my family to Oxford in 2004, and was interested to ask my children (now 15 and 18) whether they felt they were Londoners or not, having lived elsewhere for a significant part of their lives. They both feel Londoners, and we have kept very close links with the capital by almost weekly visits, which I note - as I write it - has been very important for me.