That depends on how you define 'the same people'. At the points at which the various groups that make up the English people (if you use the definition that fell out of usage in the 1950s), came together, they were culturally significantly different from one another and that would have been highly obvious to anyone living at the time.
Unless used as part of a term to denote a combination, such as Anglo-Scottish or Anglo-Italian, the term Anglo has attracted some negative connotations. 'Anglo-Saxon' for example has been suggested to be a racist term, partly due to its use in 19th century racial theories, which have been scientifically dismissed, and to cast the 'Celtic' (also an inaccurate term) peoples as outsiders. It has also been dismissed as being inaccurate as a historical term. This latter point, although technically true, I don't agree with because it's replacement term 'early medieval' is even less accurate. I addressed this point in a book I had published recently. Nonetheless, the description of your 'cake' as 'Anglo' is jarring on the basis that, generally, academic thought is now moving towards it use only to describe the Angles (so Crosby, being of Old Norse or Gaelic origin can't be Anglo) and because a much more accurate word, English, exists to describe things from or of England.
