From where I stand these sorts of labels are divisive if not racist. OK, I'm white, English and atheist, does that mean I should be called an English Atheist? Following this line there's no such thing as an English Muslim or an English Catholic either. If you are English you have freedom of religion so it becomes irrelevant!
As for ethnic divisions, they are just as divisive, if you are born in England and carry an English passport you are English, regardless of ethnic origin. If someone has chosen to live in England then they have chosen to become English and should conduct themselves accordingly.
Before anyone says anything, I'm proud to be English first, British second and European third. I make no apologies for being English and nor should anyone make any apologies for being Welsh, Scottish, Caribbean, Pakistani or Indian etc. We can all be proud of our ethnic origins, but we shouldn't lose sight of the fact that we owe our allegiance to the country in which we live! If anyone feels that they can't do that in England, then they should live in the country that commands their allegiance.