Not only Gaels from Gaelicia went to Ireland but also the Belgae. They even founded the greatest port of ancient Ireland back then, Menapia IIRC.

If you search a bit about Ireland with the search option in top menu, you'll find many interesting old topics in which Ranika writes almost complete books about stuff like this. You'll also find great posts written by Anthony. Both are experts on the history of Ireland, Celts, etc,... To bad you can't read all the interesting posts of the EBHQ. Cause thier posts are much more interesting then most books or tv programmes.