Hello, I just saw your post, and I don't know if your question has been answered in full already (I haven't read the follow-ups to your post yet), so I thought I'd tell you what I could about this since I am in a very similar boat.
I was born in the US in 73 to one American and one Brit. A few years ago, after some rigorous enquiries, I discovered that I was technically a British Citizen under British law, and that all I had to do to settle in Britain as "one of the flock" was to apply for a British Passport, which I got a year ago. Here is what I had to do to get that Passport...
I needed these documents:
My official birth certificate, with the names of both my parents.My father's (who is my British parent)
birth certificate, which I ordered via telephone from the GRO (General Registry Office) and got in two weeks. This was to prove the father who appears on my birth certicate was born in Britain.
My parents' official marriage license. Make sure it is issued by the state where they were married, not by the church. They will reject a church certificate -- I should know b/c they sent the one I gave them back and I had to apply to Iowa to give me an official one. That cost ten bucks and two weeks of time to get here. This links my birth to my father's through his marriage to my mother.
My father's British Passport. Obviously this proves he is a British citizen. I had to get my dad to renew his childhood passport to do this.
Every single Passport I have ever had. Four Passport sized photos of myself.Two letters affirming my identity, from a person from a list of 'accepted professions' you will find on your Passport app. when you get it. Each of these letters had to have a photo of me stapled on it, with this statement on the back, written by the authors of my 'identity letters.' the statement goes "I certify that this is a true likeness of ----."
A written statement from my mother and father, stating they did indeed marry, and that I was in fact their son.
It took that, and about 100 US dollars for the fee. I had my UK Passport back in about ten days -- it was hard to get all those documents together, but once I had them it was a simple and straightforward procedure.
I got all the information on that I could ever use from this site:
www.britainusa.com -- and usually when you call the British Embassy in the states, they just refer you to that webpage anyway, so you might have already got it
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At any rate, please feel free to get in touch with me if you have any questions about the process. All my friends thought I was a crazy liar when I told them I was getting a UK Passport, but I got to kick the sand right back in their faces -- KICK!! Ha-ha-ha! I myself was even worried the whole time that this was to good to be true and they'd find some reason to deny me. Not so!
Now they'll have their hands full once I get there!