I'm EE as well. I've been quite a while here but still have an accent, and because I tend to also parrot the accent of people I am with,after 10 years it's not easily recognisable as such. Most people assume places like Canada,South Africa,Australia etc. Nah,nothing so exotic.
So I had A LOT of conversations going like this:
Random(friendly,smiling): ohhh where are you from?
Me: city in England I'm living at the time
Random: no no, WHERE are you from? I love your accent!
Me: EE country
Random(face falls) : oh, I thought you were from Canada/South Africa/Australia/etc ....promptly fucks off,not interested in any more conversation.
I've also had the "funny" jokes of people pointing at beggars/women on street corners/sellers of random shit " Oh,look there's your lot!"
I've been asked if I'm DD's nanny after saying where I'm from.
I've been told in sneery tones by a bank manager that "I've done well for myself" when form filling and giving the details of my house owning,English boyfriend.
Fuck that shit dude, I'm from Kent. Deal with it.