Invasion won, granted. But "Celts eliminated"? Perhaps clarification is needed.
The (non-Celt?) Picts completely disappeared long ago, culturally and linguistically. The (Celt) Cornish have more recently disappeared culturally and almost completely linguistically. But the (Celt) Manx, Welsh and Gaels are still there -- fighting assimilation (as are the Breton Celts), but still there.
Agus tha Ga\idhlig beo\ fhathast!