I think the premise is flawed: what is a "true" englishman?
There are many tensions (and I mean this in the sense of things to base identity on rather than sources of conflict) in contemporary British society: London vs the Regions, Religion, Ethnicity, Class, Manufacturing vs Services, Post-colonialism, etc. I can't see how a single identity can hope to reconcile them. We are, after all, a country of about 50 million.
Moreover, the identity "English" is very very weak. I can't help thinking of the words of Stevie Smith:
"England, you've been here too long, And the songs you sing are the songs you sung On a braver day, now they are wrong."
People have alas seemed to take this too much to heart. What is good, and best about England, is the sheer beauty of the land which seems to conceal myth in every corner from the Towans of Kernow to the lakes of Cumbria. People have oddly identified the "upper-class" accent as attractive, whatever they mean by "the" upper-class accent. I think I prefer the authenticity of the regional accents, because for me the classism is the most unattractive feature of the English.
The greatest Englishmen: Matthew Boulton, Erasmus and Charles Darwin, Brunel, Turing, Keynes, G H Hardy, Bertrand Russell... there are many more. The English inventiveness... and humanity. Inventiveness poetry and humanity are our best traits; officiousness boorishness and snobbery are our worst.
I'll be sorry to leave England again for the US---they're such different cultures but each utterly fascinating.