I wouldn't say I sound "british", however, I think my phrases and word choices have changed a bit. I was talking to my flatmate about this topic the other day actually. It might even be the tone that goes up at times (on some words), in a more british way. If anything I sound more "neutral" than anything.
To british people I usually sound American, but to some Americans I meet...well they can't place my accent. I've definitely had quite a few people over the last year say I don't sound American. I've heard south african, kiwi, irish, scottish, amongst other things.
I also think it depends who I'm talking to. At work surrounded by my British colleagues, I probably sound and use more British words etc. When I'm at home or talking to friends maybe a bit more American. I do kind of feel like a mut accent wise. I definitely don't sound the same, for when I went home in December I heard a lot of remarks, mainly making fun of me or a word I used.
I think it's inevitable though to some degree. Maybe sooner for some than others. There is no way, at least I don't think, that one does not pick up the local lingo to some degree! It is what it is!
So like I said, I definitely sound more neutral than I did before. I use both British and American words, both slip out at times!