As a "related entity" Jersey had access to the common market, although you are right they were not part of the EU as such.Jersey isn’t in the U.K, and has never been part of the EU. Kind of makes me believe that the original story isn’t true though I’ll leave that to the experts.
I wonder how this effects other zoos in the UK? Overall it does not help in managing populations in European zoos generally.
Durrell does most of it's serious conservation breeding in range countries, so fortunately this would not have a significant effect on their conservation work.