I have lived here (southern England) for over 20 years, and in Switzerland for 5 years before that, but my American accent will never leave me. I understand that once you are an adult you are pretty much stuck with your original accent, and I don't mind too much, except for people in London (or other cities) assuming I am an obnoxious American tourist.
My voice itself, on the other hand, is apparently very nice. When living in Switzerland, a company making promotional videos called the American Women's Club, looking for someone to do a voiceover in that accent. I got the job and was subsequently called back by them several more times.
Until I was in my forties, I used to get cold callers asking for my mother, when I answered the phone. They got a sharp "You'd need to call her house to find that out" and a hang up. Now, regarding my accent, it has apparently 'softened' as some of my nicer locals say, which pleases me.