This is what the contributor to ODNB has to say:
Patricius, or Patrick, was born in the late fourth or first half of the fifth century in Roman Britain, that is, south of Hadrian's Wall. His father, Calpornius, was a deacon; his grandfather, Potitus, a priest. His mother may have been called Concessa. Patrick's family were of free birth and belonged to the local gentry. In addition to (or perhaps before) being a deacon, his father was a decurion, that is, a member of a 'city' council. Calpornius lived at the vicus ('small town') 'Bannauem Taburniae' (or 'Bannauem Taberniae'), owning a nearby country estate (villula) run by slaves, which was where Patrick was captured by Irish pirates (see below). Emendation to 'Bannaventa Berniae' produces a plausible place name, but it still cannot be securely identified: Bannaventa near Daventry is too far from the coast for Irish raids; the Banna on Hadrian's Wall, now identified with Birdoswald, is on a military frontier with no appropriate villa sites nearby. The villa could well have been in south-west Britain, or perhaps somewhere not too far from the coast between Chester and the Solway Firth; Wales is unlikely.
People round here would object to that off-hand dismissal, with no reasons given for it. The Irish influence in this region after the Romans left was strong. I still believe that Banwen has as good a claim as any place to be Patrick's original home. It will be objected that no villa has been found in the Dulais valley. I would counter that there has been no serious digging there, which is not exactly a trendy area for archaeology.
Anyway, whether Patrick was from England or Wales, he was still an immigrant to Ireland, which gave current Taoiseach Enda Kenny an opportunity to lecture Donald Trump on the subject.