Honestly English having very little Celtic influence is to be expected and isn’t considered all that unusual, at least not by historians such as N. Higham and J. Davies.

This video goes into more detail on the subject but in short, elite, “high-prestige” and (typically) conquering languages generally do not borrow all that much from the low-level conquered ones. There are exceptions of course, such as French and Gaulish, but for the vast majority of conquering languages it does seem to be the case.