You obviously can't assimilate if there's no other group present to assimilate with.

Goidelic and Brittonic replaced pre-Celtic languages everywhere in Britain. So also there must have been a considerable influx of Celtic-speakers ("Celts" by definition).

Since the native population assimilated to the newcomers rather than the other way around, the newcomers must eventually have occupied the dominant sociopoliticalposition.

The usual reason that people abandon their native language is that it's socially advantageous - if not compulsory - to do so.