Not true. They were a “Germanic” tribe during the times of the Roman Empire, buy they were not the same people we refer to today as “Germans”... there was a lot more movement and migration in ancient times.
The Angles and Saxons were the Germanic tribes which invaded Great Britain after the fall of the Roman Empire. And they became the dominant groups in what became England. There were also the native Brits who survived the invasions along with descendants of Viking invaders who decided to settle down in GB.
Anglo-Saxon is an accurate term (though very un-PC) to describe the dominant European settlement of what is now the USA, and about 90% of the white population during the revolutionary war were English.
Churchill wrote many soaring lines about the Anglo-Saxon influence in the old and new worlds.
But though a very descriptive term to describe the dominant influences of England and colonial America, Anglo-Saxon would be uber UN-PC these days.