Does not look good. Consult an immigration lawyer, but I would think that as your parents were serving US military personnel on rotation and neither was a UK citizen, you would not have gained the right to UK citizenship merely by being born on UK soil.
Since the British Nationality Act of 1981 came into force, being born in the UK does not automatically result in the acquisition of British Citizenship.
In general,
since 1 January 1983, it has been possible to acquire British citizenship automatically:
1. by birth in the UK to a parent who is
either a British citizen or
settled in the UK under immigration law;
2. by adoption in the UK by a British citizen parent;
3. by birth outside the UK to a parent who is a British citizen "otherwise than by descent";
4. by birth outside the UK to a British citizen parent in Crown, Designated or European Community service.
Try this site
http://www.legislationline.org/?tid=11&jid=54&less=false