Historians now know that the transition from post-Roman Celtic Britain to Anglo Saxon England was more complicated than Germanic-speaking invaders simply coming in and displacing the Romano-British population until that culture survived only in Wales and Cornwall. However, the British language(s) seem to have only given place names and some words for geographic features to the English language. If it was really a process of immigration and absorption of British speakers into the new English culture, where are all the Celtic loan words English would have gained during that time?
Lots of place names in England are derived from Celtic. The situation in England is pretty similar to the situation in America with Native American languages. There is extensive borrowing of Native American place names but negligible influence on American English vocabulary. For example, I'm from Ohio. I was born in Chillicothe, lived part of my life in Wapakoneta, and now live temporarily in the Kanawha valley in West Virginia.
Doesn't the evidence support displacement rather than absorption? If not, why is there so little borrowing from Celtic?