Catso is correct, and its true, we are a mongrel race, same as in America,
To be English, both your parents have to have been born here, otherwies your British.
As an Example, I joined the Armed Forces in 1966, My Father was born here, my mother wasn't, on my passport, issued by the Army, and on my identity card, my nationality was 'British/English', because my father was English, and my mother, as a first generation immigrant, was classed only as British.
To cofuse marrers further, as I said, I am British/Englis, but having been born here, and my wife also having been born here, my daughter is full blooded English.
Others may dispute my explanation, but I assure you, it is correct.