although IRL-UK routes are thought to be some of the most profitable in the network.
Remember the IRL-UK market (largely DUB market) has changed a lot since 2006/7 and routes once profitable are now heavily loss making.
Their HQ is in Ireland, all their staff are on Irish contracts, they pay tax in Ireland, they operate on an Irish AOC, and their aircraft are registered in Ireland. While they are very much spread across Europe, they are by all means an Irish airline.
Many UK based staff are on UK contracts and the UK is probably the largest or close to it for FR employment.