I was born in England to a British citizen mother. I was adopted by US military family stationed in England when I was a child and later became a US naturalized citizen. Can I get a dual citizenship status? Would I be eligible for a British passport?
If you were born in the UK to at least one British citizen parent, you were automatically a British citizen at birth. (And, in fact, if you were born in the UK before 1983, you were a British citizen at birth even without a British citizen parent. The status was called different names prior to 1983, but for someone born in the UK, the equivalent prior status turned into "British citizen" in 1983.)
British citizenship (or the equivalent prior status) is not lost upon being adopted or being naturalized in a foreign country (assuming you naturalized on or after 1949). So you are still a British citizen now, and you can apply for a British passport at any time. That you no longer have a legal parent-child relationship with your biological parents now is irrelevant -- your British citizenship was obtained automatically at the time of your birth, based on the situation at the time of your birth.