Well your last point is exactly that. I don't have the Iranian culture in me, so I suppose I identify with England more because of it. But there's a lot of Turkish culture and that runs through the whole of north London, even English people know Turkish over here!
A fellow North London British-Turk here...
I must say I do understand where you are coming from in general, although it may appear somewhat confusing to most people.
This topic has come up in the past on here and I distinctly remember someone calling me a 'questionable citizen' because I didn't class myself as 'English', even though I was born here.
To begin with, I think there is a bit of confusion in regards to this. It's not that we are rejecting England or English people, why would we? So please don't take it offensively, it's simply a case of having strong attachments to your roots and background.
Also, I can't speak on behalf of Genius Me, but in the past ever since I was a child, there have been times where I have been rejected as being 'English' or even 'British' for that matter. I remember supporting England as a kid and being asked by (English) people at school as to why I wore England kits, when I wasn't even English. Almost like I was trying to be someone I'm not. Whilst that was a long time ago, similar incidents still happen even today. I think even my English friends still class me as Turkish rather than English too.
With all that said, if I was a young footballer who had the option of choosing to play for England or Turkey, I would be happy playing for either.