Is it true to say that the english are not a celtic race?

well, none of us are actually 'celtic' if you take 'celtic' at its face value--an Iron Age people who originated in Hallstatt,Austria! (There is no evidence of huge migrations from this area into Britain and even less into Ireland.) The peoples of the British Isles and Ireland are mainly descended from hunter gatherers and neolithic farmers who came up the western seaboard from Iberia through Northern France. This includes the English, although they do have more admixture due to their closer proximity to the continent. A recent 2010 study by Irish anthropologists stated that the Germanic component in England could be as low as 20%. the Anglo-Saxon and Norse bits tend to be in the east/north-east,whereas all the West is strongly 'native.'