According to Category:British Isles, "it is more appropriate to categorize Great Britain (England, Scotland and Wales) and Ireland together as the British Isles in terms of referring to them as a nation". While I completely agree that "magical government jurisdiction can and does differ from Muggle government jurisdiction" (take Transylvania for example), this sounds a lot like ungrounded speculation to me.
If (as the article says) the MoM's full title is the "Ministry of Magic of the United Kingdom", and the British and Irish Quidditch League comes under the authority of the Department of Magical Games and Sports, with Fudge accepting the Trophy on behalf of Ireland in 1994, then I'd say there's a better case for supposing that the United Kingdom in the HP universe includes Ireland than for supposing a hypothetical "British Isles" Wizarding nation.
Historically this was the case in the real world, so this could easily be explained if Ireland never seceded from the U.K. in the HP universe. Political divisions in Ireland are something that JKR would definitely have wanted to avoid, especially at the time she was writing, and correct me if I'm wrong but I don't think there are any direct references to Northern or Southern Ireland in the series, just to Ireland itself. From an in-universe perspective, regardless of the extent of the Muggle U.K., I doubt the wizards of an independent Ireland would allow themselves to be governed by the U.K. Ministry.
On a more practical note, with many new readers unfamiliar with the complicated relationship between Great Britain, Ireland, the U.K., Eire, England, Northern Ireland, Scotland and Wales, it might help to make it clearer if we had a United Kingdom article, and tidied up the existing articles too; the "Known locations" section of Great Britain for example is way too long and is just repeated in each country and county article, with no sense of the locations' notability. --xensyriaT 22:51, November 28, 2012 (UTC)