Overall, the U.K. accounts for a sixth of Irish exports, Sullivan told CNBC over the phone. It is the biggest market for Irish food exports and the U.K. also plays a crucial role for the Irish tourism sector. The Dublin to London pair - flights between all airports in London and Dublin Airport - is the busiest air route in Europe and the second busiest international air route in the world.
Irish businesses share such concerns. "Brexit is going to be an issue for us as we look forward," Tony Smurfit, chief executive officer at Smurfit Kappa, told CNBC on Wednesday.
The head of the world's leader in paper-based packing, headquartered in Dublin, added: "I think right now we aren't seeing any particular demand issues, but when you look at our Irish business, when we export from Ireland into the U.K. that's going to affect us, unless we get price increases."