There is no such thing as biological ethnicity, period. Genealogical companies use the word "ethnicity" to describe DNA which is a huge misnomer. Your ethnicity is your cultural identity. So yes, there is such a thing as English ethnicity: People can identify with "English" as their culture. But there is no such thing as "biological Englishness". The idea of such a thing is a racist myth.

(This answer is short but there's not much more to say...)