Why do most English people look like non-Nordics when their ancestors were Anglo-Saxons from northern Germany?

I have been to London England and I have to say that a vast majority of the native Brits there don't look like your typical northern Germanic physical type. A lot of them have brown hair and brown eyes (they look more like northern Spaniards). Even the typical Celtic look (red hair and green eyes) are not even that predominant. Why is this so? Could it be that the Nordics and Celts were the minority invaders while the vast majority of people who already settled there were non-Indo-European neolithic people?