We are beginning to have an obsession with "ethnicity". It shouldn't matter where your parents or grandparents or great-grandparents are from, what matters is where we are now. Where we are now is that we are all British.
In some cases (such as on medical grounds) ethnicity can play a part – but as far as the Irish go, this is clearly not the case. As an English person of "Irish descent" I'm fed up of the confusion. We should either have "ethnic" monitoring for whether someone is English, Irish, Scottish or Welsh (dependent on place of birth or whatever other justification you choose) – or we should just leave the ethnic monitoring selection as "white" or "white British". Why should the Irish have more importance than any other country either in the former British Isles or in the rest of Europe?