Good point, Brian. I doubt whether it makes much sense to talk about 'imperialism' or 'empires' (except the Holy Roman one, perhaps) in feudal Europe. But I'm afraid my historical knowledge is now running up against the buffers!

Anyway, from the accession of John in 1199, the King of England was 'Lord' and (from 1541) 'King' of Ireland.

I have checked the issue about the origin of the Irish Celts. As I suspected there appears to have been an early (i.e. first millenium BCE) division between the Q-Celts (Gaels, 'Scots') who established themselves in Ireland and later invaded what is now Scotland, and the P-Celts ('Ancient Britons') who settled in Britain and spoke a precursor of Welsh, Cornish and Breton. Irish legend suggests that the Gaels originally came from Spain rather from Britain.