There is a lot of overlap between Great Britain and Ireland in DNA results (this type of thing is especially common in people from adjacent European regions). In addition to this most probable factor, you might have quite a few distant Irish ancestors who, at some point in time, crossed over and settled in England too.

Both Great Britain and Ireland share common ancestors from the original pre-Celtic inhabitants, who were closely related to the modern Basques of northern Spain/southern France, as well as people generally regarded as Celts (i.e. Scots, Britons, Gaels, and other tribes who spoke Celtic languages and who were present in Britain and Ireland before the Romans, Anglo-Saxons, Vikings, or anyone else came).