Celtic loan words survived to become a part of Anglo-Saxon English. The Old English word rice--a noun meaning "kingdom" (cf. Ger. Reich), is almost certainly Celtic in origin, but this word was probably adapted by Germanic tribes on the continent long before the Anglo-Saxons settled in Britain. A few other Old English words such as ambeht ("servant"), and dun ("hill, down") might be Celtic loan-words
The Anglo-Saxons borrowed these words and used them for a few centuries, but these later fell out of common use. They simply didn't "stick" linguistically.
In general, two types of Celtic loan words were likely targets of permanent Anglo-Saxon adaptation before the Norman Conquest: