I think you're conflating modern national identity with ethnolinguistic groups. It's true that England was invaded by many Germanic peoples such as the Angles, Saxons, and Normans, but Germanic and German are different. Germanic refers to an ethnolinguistic group that is currently prevalent in Central Europe, Scandinavia, and, of course, Great Britain. There isn't really an ethic English or ethnic German group of people. Just because many people in England today are predominantly Germanic and not Celtic doesn't make them any less English. Celtic =/= English and Germanic =/= German.