Annex 2 aircraft are those that are operated in compliance with Permit certification from the Light Aircraft Association (LAA) or, the CAA here in GB.
Not all Annex 2 aircraft are on a permit (LAA or CAA). For example, Piper PA22's are Annex 2 but on a C of A.
In places like France the situation is at least as complicated with for instance Gardans moving from Annex I to a restricted C of A category, still administered by DGAC
As I understand it, some of the Gardan Horizons in the UK are on an EASA C of A and some (one?) are on an EASA permit administered by the LAA.