Indeed Terpe, the EU/EAA permit applies to all applicants who are a family member of an Eu/EAA national traveling together to any EU country except the one the EU national is a national of (that would be Brits returning to the UK for inatance). Though in specific cases it also applies to them: those who exercised their freedom of movement right in an other EU/EAA country and returning, this is known as -among other names- as the Surrinder Sighn route.

The UKVI page on EAA permit should tell you all you need to know, if in doubt or you wish to read more you could check the EU webpage on travel to the EU with family members:
http://europa.eu/youreurope/citizens...y/index_en.htm

And if you really wish to dig into it you could read the EU directive that this all is based on: freedom of movement (2004/38/EC).

Short answer: if you are not a British national but just Irish (or any other EU nationality) your wife id eligible for this free and swiftly issued visa.