Firstly, the English and Irish are not both derived from Celts. Even the article you posted stated this.
Secondly, in any event, this in my opinion would not be the main reason as to why Northern Ireland is different to Cyprus. Largely because the conflict in Northern Ireland is more religious than ethnic. Ethnicity does not play a large role as you imply. Many of the Protestants in Northern Ireland are of Scottish rather than English origin anyway. Cyprus is largely an ethnic conflict. Moreover, there are many reasons that I believe rank well above the reason you give.
In Cyprus, the Greek Cypriots were the majority population all over the island since the Classical times up until 1974, in Northern Ireland, the Protestants make up the majority and have done for hundreds of years. They wish to remain in the UK. When the British gave Ireland independence, the Northern part opted to stay in the UK. Again, completely different to Cyprus. There is evidence that Ulster (which covers Northern Ireland) has always been a distinct region of Ireland. Again, no comparison to Cyprus. Britain has said that the future of Northern Ireland will be decided by the Northern Ireland people, again, no relevance to Cyprus, where Turkey pulls the strings. Britain allows power-sharing based on true democratic principles in Northern Ireland, again, no comparison in Cyprus. With Northern Ireland, there was no recent invasion contrary to international law that caused the mass displacement of indigenious Irish people, to move in British people. Yes, before you go off to do your research, I am aware of the Plantation of Ulster, but this occurred 400 years ago, which was a completely different time and era, without the international standards that existed in 1974. The Protestants in Ulster have been in Ireland for about as long as Turkish Cypriots have been in Cyprus.
Whilst I accept that there are some small similarities, there are also huge differences. Cyprus has been internationally recognised as illegally occupied; there is no equivalent in Northern Ireland. I support the British government's view, that the future of Northern Ireland should be decided by its people. The British government actually supported the Irish Republicans having a power-sharing agreement with the Unionists, which is something that the Unionists originally did not want. Finally, and perhaps most importantly, I get the impression that the British would be happy to dispose of Northern Ireland and the problem that it brings, but they know, to do so, would eradicate all the progress Northern Ireland has made and cause a civil war.