I did hear somewhere (it may not be true) that when DNA was analysed there was no significant differences in DNA between average British and average Celtic (i.e. Irish, Welsh, Scots, Cornish etc). This means that there are no significant 'racial' characteristics that differentiate between British and Irish people. This is not surprising when you consider that about a third of English people are descended, at least partially from Irish people, however not too many of them claim Irish heritage in the same way that people from the USA do. It's an interesting area and I guess that most people define themselves as being in the group that they want to be in, the truth often being a bit more mundane.