"it's not fashionable for the English to acknowledge their Celtic past let alone claim it as part of their identity"
Boadicea? Isn't there a statue opposite Westminster? King Arthur? A round table in Winchester?
Seems to me that the English are perfectly happy with their Celtic past and Norman/French/German rulers, but are embarrassed to mention their real Anglo-Saxon history, preferring to rely on some pre-Roman idylls and the glories(?) of the Vikings. (This seems even more true of Scotland, with their romantic highland fantasies. Please go start another thread if you object to that.)
This is on a par with the snubbing of English folk music (though I'm not suggesting that goes back to the Anglo-Saxons).