There is a very good book called Imagining Roman Britain by Virginia Hoselitz that goes into some detail about this, because during the nineteenth century British scholars, being nineteenth century British scholars, frequently debated about where the "origins" and the "essential character" of the British people came from. The debates were in intellectual and antiquarian terms but tended to come down to politics. The Normans were out because they were French, and that wouldn't do at all. Several of the more Romantic inclined favored the Celts (or rather the pre-Roman Britons if they wanted to downplay the European angle) because of their lovely and somewhat enigmatic art and the tales of heroism such as Caractacus and Boudicca. A major problem of course is that they lost, which doesn't reflect well on a global empire. I also suspect that the status of the welsh and Irish had a hand in it as well but I don't recall that specifically. The Romans being the essential originators was attractive, particularly because there was a lot of ideological linking of the Roman and British empires as great spreaders of civilization. The problem with them, of course, is that there isn't much distinctly British about them. The Anglo-Saxons, then emerged as the ones that can be claimed as truly distinctively British.

It is a bit more complicated but it basically boils down to politics and ideology.