That's pretty funny. But I never had British people snicker at me. She was my first English teacher (English is the first language I learned and knew for years). I guess I blended in pretty well when I went to London for family holidays.
That's probably because having "British" accented English is never considered a bad thing in the English-speaking world. It is like the "top-shelf brand" of English accents.
I read and studied Shakespeare and watched endless amounts of the BBC when I was a child, and was a stickler for proper pronunciation - so much so that my classmates in the American South were convinced I was really British, but all I was really doing was enunciating and pronouncing each word clearly and distinctly. I wasn't even using British words - just American Standard, but in the South where drawling and blending words together was the norm, that was enough to separate me!
I still remember how embarrassed my mother would get - she has a very thick Southern accent, and people would always look at her confused after she introduced me as her son and I spoke to them in a completely different accent! We visited Canada when I was ten and I had a long conversation with a man who asked if I lived nearby - and then my mother walked up and said something and he immediately placed her as coming from the American South, then proceeded to laugh until he bent double when he found I was her son. I still remember being proud that he had thought I was Canadian. (Note: I have never, nor will I, ever end a sentence in 'eh?' I couldn't do it with a straight face anyway.)
Since I've been a teen, I've adopted the better strategy of using whatever English accent of the group I am currently with. If I am in the South, I drawl and say "y'all" and generally just get lazy and speak what comes naturally - which growing up in the South, is a natural Southern accent in my case. I sometimes slip into that accent if I'm very tired.
However, if I am up North, or in Canada, or any professional environment, I adopt the very clear American Standard accent that News Casters are fond of using. I consider it a courtesy to adopt the language or manner of speech where ever I am visiting to facilitate better communication. I'm always careful to not come across as mocking though, because I know how annoying people faking your accent can be, since I hate the fake Southern accents I hear on TV and in movies. The people that fake a Southern accent always come across as trying WAY too hard, and it makes them sound mentally deficient. That and it seems that most consider "Gone with the Wind" appropriate reference for a Southern accent, when no one in the South has spoken that way for a 100 years or more.
I have found it funny when I met an Australian girl who kept cooing over my "accent". Cue the standard - "I don't have an accent! You do!"