The truth is there is a lot of British blood in the Irish, and a lot of Irish blood in the British.
Looks like I don't qualify.
It appears that here in New Zealand British and Irish descents don't differentiate each other too much. Everyone seems to have mixed into a generic British-Irish descents and the indicator of their father's ancestry seems to be their nominal religious affiliation.
In the United States it is the other story - people would classify quite deeply into Scots-Irish, Irish, English etc. The anti-British attotudes of some otherwise politically conservative Irish-Americans also astounds me. Their rhetorics read like apologists of the hardline IRA for instance which Irish descent Australians on a whole would not make. Meanwhile in New Zealand it seems the Irish descents have made peace with the British descents.