Honeybee, the UK makes a distinction between citizenship by descent and citizenship otherwise than by descent.
Basically, the reason for the distinction is to cut off the passage of citizenship one generation out of the UK.
If your dad was born in the US and you were as well, then it would also be important to know when both of you were born.
Check with Garry on this one, because it involves looking at British nationality law at several points in time. My suspicion however is that neither of you would be eligible.