the pre-print of a new article on Irish genes, based on studies of the modern population. They find, first of all, that the Irish are clearly distinguishable, genetically, from the rest of Britain; the biggest division in their dataset is between the two islands. The Xes in the diagram above are representations of individual genomes arranged according to variation; the colors represent groupings in the data. You can see that the distance between the genomes, by variation, roughly maps out the British Isles. Note that while southern Britain is a long way from southern Ireland, northern Ireland and western Scotland overlap.
Note that Orkney is a serious outlier, quite different from England, Scotland, or Ireland. And this is not just because of the Vikings; even excluding their genes, Orkney still stands out.