With respect to the DNA debate about identity, Britishness is a bit odd here.
As a term, it is derived from 'Britannic' - used by Aristotle and other classical writers to refer to the islands Ierna and Albion.
The term 'Irish' is the English (not British) term that came to be used for the term 'Scotti' - the term by which the inhabitants of the island were once known (although Gerald of Wales refers to two tribes, the 'Gaelige' and the 'Scotti').
The Scotti, however, gave their name to Caledonia (now Scotland), the land of the Scotti. That would account for the great similarity in DNA make-up between the inhabitants of Scotland and Northern Ireland.
The Britons, such as St Patrick, were Celts. And it is the Britons who, in a well-known Welsh anthem, are prophesised to put the Saxons down. Some saw Henry VIII, with his Welsh, or Celtic, or British, ancestry fulfilling this, as perhaps Henry did in laying claim to a 'Britannic Majesty' in these islands.
W A MILLER